LMFDB - Embedded newform 72.3.j.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.12
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.390748 + 1.96146i) q^{2} +(-0.102534 - 2.99825i) q^{3} +(-3.69463 - 1.53287i) q^{4} +(-3.47699 - 6.02232i) q^{5} +(5.92100 + 0.970445i) q^{6} +(2.29534 - 3.97565i) q^{7} +(4.45034 - 6.64790i) q^{8} +(-8.97897 + 0.614843i) q^{9} +O(q^{10})$	\(q+(-0.390748 + 1.96146i) q^{2} +(-0.102534 - 2.99825i) q^{3} +(-3.69463 - 1.53287i) q^{4} +(-3.47699 - 6.02232i) q^{5} +(5.92100 + 0.970445i) q^{6} +(2.29534 - 3.97565i) q^{7} +(4.45034 - 6.64790i) q^{8} +(-8.97897 + 0.614843i) q^{9} +(13.1711 - 4.46675i) q^{10} +(-7.77003 + 13.4581i) q^{11} +(-4.21711 + 11.2346i) q^{12} +(19.3855 - 11.1922i) q^{13} +(6.90117 + 6.05570i) q^{14} +(-17.6999 + 11.0424i) q^{15} +(11.3006 + 11.3268i) q^{16} -9.17185i q^{17} +(2.30253 - 17.8521i) q^{18} -4.53461i q^{19} +(3.61474 + 27.5800i) q^{20} +(-12.1553 - 6.47437i) q^{21} +(-23.3614 - 20.4993i) q^{22} +(-2.69533 + 1.55615i) q^{23} +(-20.3883 - 12.6616i) q^{24} +(-11.6789 + 20.2284i) q^{25} +(14.3782 + 42.3973i) q^{26} +(2.76410 + 26.8581i) q^{27} +(-14.5746 + 11.1701i) q^{28} +(6.42846 - 11.1344i) q^{29} +(-14.7429 - 39.0324i) q^{30} +(-2.17666 - 3.77008i) q^{31} +(-26.6327 + 17.7397i) q^{32} +(41.1474 + 21.9166i) q^{33} +(17.9902 + 3.58388i) q^{34} -31.9235 q^{35} +(34.1165 + 11.4920i) q^{36} -23.0374i q^{37} +(8.89444 + 1.77189i) q^{38} +(-35.5448 - 56.9751i) q^{39} +(-55.5095 - 3.68669i) q^{40} +(60.6979 - 35.0439i) q^{41} +(17.4489 - 21.3123i) q^{42} +(51.7345 + 29.8689i) q^{43} +(49.3370 - 37.8122i) q^{44} +(34.9226 + 51.9364i) q^{45} +(-1.99913 - 5.89484i) q^{46} +(32.1187 + 18.5438i) q^{47} +(32.8019 - 35.0434i) q^{48} +(13.9628 + 24.1843i) q^{49} +(-35.1136 - 30.8118i) q^{50} +(-27.4995 + 0.940424i) q^{51} +(-88.7787 + 11.6357i) q^{52} -24.3319 q^{53} +(-53.7612 - 5.07311i) q^{54} +108.065 q^{55} +(-16.2147 - 32.9522i) q^{56} +(-13.5959 + 0.464951i) q^{57} +(19.3278 + 16.9599i) q^{58} +(-20.7560 - 35.9504i) q^{59} +(82.3211 - 13.6658i) q^{60} +(-34.6245 - 19.9904i) q^{61} +(8.24537 - 2.79626i) q^{62} +(-18.1654 + 37.1086i) q^{63} +(-24.3890 - 59.1707i) q^{64} +(-134.807 - 77.8306i) q^{65} +(-59.0667 + 72.1450i) q^{66} +(-24.3421 + 14.0539i) q^{67} +(-14.0593 + 33.8866i) q^{68} +(4.94209 + 7.92171i) q^{69} +(12.4741 - 62.6167i) q^{70} +59.8148i q^{71} +(-35.8720 + 62.4275i) q^{72} -53.8883 q^{73} +(45.1869 + 9.00183i) q^{74} +(61.8472 + 32.9420i) q^{75} +(-6.95098 + 16.7537i) q^{76} +(35.6698 + 61.7819i) q^{77} +(125.643 - 47.4567i) q^{78} +(-0.557280 + 0.965237i) q^{79} +(28.9215 - 107.439i) q^{80} +(80.2439 - 11.0413i) q^{81} +(45.0196 + 132.750i) q^{82} +(39.8750 - 69.0655i) q^{83} +(34.9851 + 42.5530i) q^{84} +(-55.2358 + 31.8904i) q^{85} +(-78.8017 + 89.8037i) q^{86} +(-34.0429 - 18.1325i) q^{87} +(54.8887 + 111.547i) q^{88} -10.6605i q^{89} +(-115.517 + 48.2050i) q^{90} -102.760i q^{91} +(12.3436 - 1.61780i) q^{92} +(-11.0804 + 6.91271i) q^{93} +(-48.9231 + 55.7536i) q^{94} +(-27.3089 + 15.7668i) q^{95} +(55.9188 + 78.0326i) q^{96} +(-72.6276 + 125.795i) q^{97} +(-52.8923 + 17.9375i) q^{98} +(61.4923 - 125.617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.390748	+	1.96146i	−0.195374	+	0.980729i
$2$	−0.390748	+	1.96146i	−0.195374	+	0.980729i
$3$	−0.102534	−	2.99825i	−0.0341779	−	0.999416i
$3$	−0.102534	−	2.99825i	−0.0341779	−	0.999416i
$4$	−3.69463	−	1.53287i	−0.923658	−	0.383218i
$5$	−3.47699	−	6.02232i	−0.695397	−	1.20446i	−0.970047	−	0.242919i	$-0.921895\pi$
$5$	−3.47699	−	6.02232i	−0.695397	−	1.20446i	0.274649	−	0.961544i	$-0.411438\pi$
$6$	5.92100	+	0.970445i	0.986833	+	0.161741i
$7$	2.29534	−	3.97565i	0.327906	−	0.567951i	−0.654190	−	0.756330i	$-0.726990\pi$
$7$	2.29534	−	3.97565i	0.327906	−	0.567951i	0.982096	+	0.188380i	$0.0603236\pi$
$8$	4.45034	−	6.64790i	0.556292	−	0.830987i
$9$	−8.97897	+	0.614843i	−0.997664	+	0.0683159i
$10$	13.1711	−	4.46675i	1.31711	−	0.446675i
$11$	−7.77003	+	13.4581i	−0.706367	+	1.22346i	0.259829	+	0.965655i	$0.416334\pi$
$11$	−7.77003	+	13.4581i	−0.706367	+	1.22346i	−0.966196	+	0.257809i	$0.917000\pi$
$12$	−4.21711	+	11.2346i	−0.351426	+	0.936216i
$13$	19.3855	−	11.1922i	1.49120	−	0.860942i	0.491246	−	0.871021i	$-0.336542\pi$
$13$	19.3855	−	11.1922i	1.49120	−	0.860942i	0.999949	+	0.0100786i	$0.00320818\pi$
$14$	6.90117	+	6.05570i	0.492941	+	0.432550i
$15$	−17.6999	+	11.0424i	−1.17999	+	0.736157i
$16$	11.3006	+	11.3268i	0.706288	+	0.707925i
$17$		−	9.17185i		−	0.539520i	−0.962928	−	0.269760i	$-0.913056\pi$
$17$		−	9.17185i		−	0.539520i	0.962928	−	0.269760i	$-0.0869444\pi$
$18$	2.30253	−	17.8521i	0.127918	−	0.991785i
$19$		−	4.53461i		−	0.238664i	−0.992854	−	0.119332i	$-0.961925\pi$
$19$		−	4.53461i		−	0.238664i	0.992854	−	0.119332i	$-0.0380752\pi$
$20$	3.61474	+	27.5800i	0.180737	+	1.37900i
$21$	−12.1553	−	6.47437i	−0.578826	−	0.308303i
$22$	−23.3614	−	20.4993i	−1.06188	−	0.931787i
$23$	−2.69533	+	1.55615i	−0.117188	+	0.0676587i	−0.557448	−	0.830212i	$-0.688220\pi$
$23$	−2.69533	+	1.55615i	−0.117188	+	0.0676587i	0.440260	+	0.897870i	$0.354886\pi$
$24$	−20.3883	−	12.6616i	−0.849514	−	0.527566i
$25$	−11.6789	+	20.2284i	−0.467155	+	0.809136i
$26$	14.3782	+	42.3973i	0.553010	+	1.63066i
$27$	2.76410	+	26.8581i	0.102374	+	0.994746i
$28$	−14.5746	+	11.1701i	−0.520522	+	0.398932i
$29$	6.42846	−	11.1344i	0.221671	−	0.383946i	−0.733644	−	0.679534i	$-0.762182\pi$
$29$	6.42846	−	11.1344i	0.221671	−	0.383946i	0.955316	+	0.295588i	$0.0955155\pi$
$30$	−14.7429	−	39.0324i	−0.491430	−	1.30108i
$31$	−2.17666	−	3.77008i	−0.0702147	−	0.121615i	0.828781	−	0.559574i	$-0.189035\pi$
$31$	−2.17666	−	3.77008i	−0.0702147	−	0.121615i	−0.898995	+	0.437958i	$0.855702\pi$
$32$	−26.6327	+	17.7397i	−0.832273	+	0.554366i
$33$	41.1474	+	21.9166i	1.24689	+	0.664139i
$34$	17.9902	+	3.58388i	0.529123	+	0.105408i
$35$	−31.9235			−0.912101
$36$	34.1165	+	11.4920i	0.947680	+	0.319222i
$37$		−	23.0374i		−	0.622633i	−0.950306	−	0.311316i	$-0.899230\pi$
$37$		−	23.0374i		−	0.622633i	0.950306	−	0.311316i	$-0.100770\pi$
$38$	8.89444	+	1.77189i	0.234064	+	0.0466287i
$39$	−35.5448	−	56.9751i	−0.911405	−	1.46090i
$40$	−55.5095	−	3.68669i	−1.38774	−	0.0921673i
$41$	60.6979	−	35.0439i	1.48044	−	0.854730i	0.480682	−	0.876895i	$-0.340389\pi$
$41$	60.6979	−	35.0439i	1.48044	−	0.854730i	0.999754	+	0.0221647i	$0.00705581\pi$
$42$	17.4489	−	21.3123i	0.415450	−	0.507437i
$43$	51.7345	+	29.8689i	1.20313	+	0.694626i	0.961249	−	0.275681i	$-0.0889034\pi$
$43$	51.7345	+	29.8689i	1.20313	+	0.694626i	0.241878	+	0.970307i	$0.422237\pi$
$44$	49.3370	−	37.8122i	1.12129	−	0.859369i
$45$	34.9226	+	51.9364i	0.776057	+	1.15414i
$46$	−1.99913	−	5.89484i	−0.0434593	−	0.128149i
$47$	32.1187	+	18.5438i	0.683377	+	0.394548i	0.801126	−	0.598495i	$-0.204235\pi$
$47$	32.1187	+	18.5438i	0.683377	+	0.394548i	−0.117749	+	0.993043i	$0.537568\pi$
$48$	32.8019	−	35.0434i	0.683372	−	0.730070i
$49$	13.9628	+	24.1843i	0.284955	+	0.493556i
$50$	−35.1136	−	30.8118i	−0.702273	−	0.616236i
$51$	−27.4995	+	0.940424i	−0.539205	+	0.0184397i
$52$	−88.7787	+	11.6357i	−1.70728	+	0.223763i
$53$	−24.3319			−0.459092			−0.229546	−	0.973298i	$-0.573724\pi$
$53$	−24.3319			−0.459092			−0.229546	+	0.973298i	$0.573724\pi$
$54$	−53.7612	−	5.07311i	−0.995577	−	0.0939465i
$55$	108.065			1.96482
$56$	−16.2147	−	32.9522i	−0.289548	−	0.588432i
$57$	−13.5959	+	0.464951i	−0.238524	+	0.00815703i
$58$	19.3278	+	16.9599i	0.333238	+	0.292412i
$59$	−20.7560	−	35.9504i	−0.351796	−	0.609329i	0.634768	−	0.772703i	$-0.281096\pi$
$59$	−20.7560	−	35.9504i	−0.351796	−	0.609329i	−0.986564	+	0.163374i	$0.947762\pi$
$60$	82.3211	−	13.6658i	1.37202	−	0.227763i
$61$	−34.6245	−	19.9904i	−0.567614	−	0.327712i	0.188582	−	0.982057i	$-0.439611\pi$
$61$	−34.6245	−	19.9904i	−0.567614	−	0.327712i	−0.756196	+	0.654345i	$0.772944\pi$
$62$	8.24537	−	2.79626i	0.132990	−	0.0451010i
$63$	−18.1654	+	37.1086i	−0.288340	+	0.589025i
$64$	−24.3890	−	59.1707i	−0.381078	−	0.924543i
$65$	−134.807	−	77.8306i	−2.07395	−	1.19739i
$66$	−59.0667	+	72.1450i	−0.894950	+	1.09311i
$67$	−24.3421	+	14.0539i	−0.363315	+	0.209760i	−0.670534	−	0.741879i	$-0.733935\pi$
$67$	−24.3421	+	14.0539i	−0.363315	+	0.209760i	0.307219	+	0.951639i	$0.400602\pi$
$68$	−14.0593	+	33.8866i	−0.206754	+	0.498332i
$69$	4.94209	+	7.92171i	0.0716244	+	0.114807i
$70$	12.4741	−	62.6167i	0.178201	−	0.894524i
$71$			59.8148i			0.842462i	0.906953	+	0.421231i	$0.138402\pi$
$71$			59.8148i			0.842462i	−0.906953	+	0.421231i	$0.861598\pi$
$72$	−35.8720	+	62.4275i	−0.498223	+	0.867049i
$73$	−53.8883			−0.738196			−0.369098	−	0.929390i	$-0.620333\pi$
$73$	−53.8883			−0.738196			−0.369098	+	0.929390i	$0.620333\pi$
$74$	45.1869	+	9.00183i	0.610634	+	0.121646i
$75$	61.8472	+	32.9420i	0.824629	+	0.439227i
$76$	−6.95098	+	16.7537i	−0.0914603	+	0.220444i
$77$	35.6698	+	61.7819i	0.463244	+	0.802363i
$78$	125.643	−	47.4567i	1.61081	−	0.608419i
$79$	−0.557280	+	0.965237i	−0.00705418	+	0.0122182i	−0.869531	−	0.493878i	$-0.835579\pi$
$79$	−0.557280	+	0.965237i	−0.00705418	+	0.0122182i	0.862477	+	0.506097i	$0.168912\pi$
$80$	28.9215	−	107.439i	0.361519	−	1.34299i
$81$	80.2439	−	11.0413i	0.990666	−	0.136313i
$82$	45.0196	+	132.750i	0.549020	+	1.61890i
$83$	39.8750	−	69.0655i	0.480422	−	0.832114i	−0.519326	−	0.854576i	$-0.673817\pi$
$83$	39.8750	−	69.0655i	0.480422	−	0.832114i	0.999748	+	0.0224616i	$0.00715035\pi$
$84$	34.9851	+	42.5530i	0.416490	+	0.506584i
$85$	−55.2358	+	31.8904i	−0.649833	+	0.375181i
$86$	−78.8017	+	89.8037i	−0.916299	+	1.04423i
$87$	−34.0429	−	18.1325i	−0.391298	−	0.208419i
$88$	54.8887	+	111.547i	0.623736	+	1.26758i
$89$		−	10.6605i		−	0.119781i	−0.998205	−	0.0598905i	$-0.980925\pi$
$89$		−	10.6605i		−	0.119781i	0.998205	−	0.0598905i	$-0.0190751\pi$
$90$	−115.517	+	48.2050i	−1.28352	+	0.535611i
$91$		−	102.760i		−	1.12923i
$92$	12.3436	−	1.61780i	0.134170	−	0.0175848i
$93$	−11.0804	+	6.91271i	−0.119145	+	0.0743302i
$94$	−48.9231	+	55.7536i	−0.520459	+	0.593123i
$95$	−27.3089	+	15.7668i	−0.287462	+	0.165966i
$96$	55.9188	+	78.0326i	0.582488	+	0.812839i
$97$	−72.6276	+	125.795i	−0.748738	+	1.29685i	0.199690	+	0.979859i	$0.436006\pi$
$97$	−72.6276	+	125.795i	−0.748738	+	1.29685i	−0.948428	+	0.316993i	$0.897327\pi$
$98$	−52.8923	+	17.9375i	−0.539718	+	0.183035i
$99$	61.4923	−	125.617i	0.621135	−	1.26886i
$100$	74.1567	−	56.8342i	0.741567	−	0.568342i
$101$	47.7840	−	82.7643i	0.473109	−	0.819449i	−0.526417	−	0.850226i	$-0.676465\pi$
$101$	47.7840	−	82.7643i	0.473109	−	0.819449i	0.999526	+	0.0307777i	$0.00979838\pi$
$102$	8.90077	−	54.3065i	0.0872625	−	0.532417i
$103$	−51.3053	−	88.8633i	−0.498109	−	0.862751i	0.501888	−	0.864933i	$-0.332639\pi$
$103$	−51.3053	−	88.8633i	−0.498109	−	0.862751i	−0.999998	+	0.00218165i	$0.999306\pi$
$104$	11.8673	−	178.682i	0.114108	−	1.71810i
$105$	3.27324	+	95.7146i	0.0311737	+	0.911568i
$106$	9.50765	−	47.7260i	0.0896948	−	0.450245i
$107$	−23.2763			−0.217536			−0.108768	−	0.994067i	$-0.534690\pi$
$107$	−23.2763			−0.217536			−0.108768	+	0.994067i	$0.534690\pi$
$108$	30.9578	−	103.468i	0.286646	−	0.958037i
$109$			83.5260i			0.766294i	0.923687	+	0.383147i	$0.125160\pi$
$109$			83.5260i			0.766294i	−0.923687	+	0.383147i	$0.874840\pi$
$110$	−42.2263	+	211.965i	−0.383876	+	1.92696i
$111$	−69.0718	+	2.36211i	−0.622269	+	0.0212803i
$112$	70.9702	−	18.9284i	0.633663	−	0.169003i
$113$	22.9401	−	13.2445i	0.203010	−	0.117208i	−0.395049	−	0.918660i	$-0.629272\pi$
$113$	22.9401	−	13.2445i	0.203010	−	0.117208i	0.598059	+	0.801452i	$0.295939\pi$
$114$	4.40059	−	26.8494i	0.0386016	−	0.235521i
$115$	18.7433	+	10.8214i	0.162985	+	0.0940994i
$116$	−40.8185	+	31.2836i	−0.351883	+	0.269686i
$117$	−167.181	+	112.414i	−1.42890	+	0.960803i
$118$	78.6255	−	26.6644i	0.666318	−	0.225969i
$119$	−36.4641	−	21.0526i	−0.306421	−	0.176912i
$120$	−5.36202	+	166.809i	−0.0446835	+	1.39008i
$121$	−60.2469	−	104.351i	−0.497908	−	0.862402i
$122$	52.7399	−	60.1032i	0.432294	−	0.492649i
$123$	−111.294	−	178.394i	−0.904829	−	1.45036i
$124$	2.26289	+	17.2656i	0.0182491	+	0.139239i
$125$	−11.4202			−0.0913620
$126$	−65.6888	−	50.1308i	−0.521339	−	0.397864i
$127$	−10.6813			−0.0841046			−0.0420523	−	0.999115i	$-0.513390\pi$
$127$	−10.6813			−0.0841046			−0.0420523	+	0.999115i	$0.513390\pi$
$128$	125.591	−	24.7172i	0.981179	−	0.193103i
$129$	84.2498	−	158.175i	0.653099	−	1.22616i
$130$	205.337	−	234.005i	1.57951	−	1.80004i
$131$	119.843	+	207.575i	0.914835	+	1.58454i	0.807143	+	0.590356i	$0.201012\pi$
$131$	119.843	+	207.575i	0.914835	+	1.58454i	0.107691	+	0.994184i	$0.465654\pi$
$132$	−118.429	−	144.047i	−0.897190	−	1.09127i
$133$	−18.0280	−	10.4085i	−0.135549	−	0.0782594i
$134$	−18.0545	−	53.2375i	−0.134735	−	0.397295i
$135$	152.138	−	110.032i	1.12694	−	0.815049i
$136$	−60.9735	−	40.8178i	−0.448334	−	0.300131i
$137$	109.882	+	63.4404i	0.802058	+	0.463069i	0.844190	−	0.536043i	$-0.180082\pi$
$137$	109.882	+	63.4404i	0.802058	+	0.463069i	−0.0421320	+	0.999112i	$0.513415\pi$
$138$	−17.4692	+	6.59830i	−0.126588	+	0.0478137i
$139$	−131.623	+	75.9927i	−0.946930	+	0.546710i	−0.892126	−	0.451787i	$-0.850787\pi$
$139$	−131.623	+	75.9927i	−0.946930	+	0.546710i	−0.0548041	+	0.998497i	$0.517453\pi$
$140$	117.946	+	48.9347i	0.842469	+	0.349534i
$141$	52.3055	−	98.2012i	0.370961	−	0.696463i
$142$	−117.324	−	23.3725i	−0.826226	−	0.164595i
$143$			347.857i			2.43256i
$144$	−108.432	−	94.7549i	−0.753000	−	0.658020i
$145$	−89.4067			−0.616598
$146$	21.0568	−	105.700i	0.144225	−	0.723970i
$147$	71.0787	−	44.3436i	0.483529	−	0.301657i
$148$	−35.3134	+	85.1147i	−0.238604	+	0.575100i
$149$	49.0244	+	84.9127i	0.329023	+	0.569884i	0.982318	−	0.187219i	$-0.0599474\pi$
$149$	49.0244	+	84.9127i	0.329023	+	0.569884i	−0.653296	+	0.757103i	$0.726614\pi$
$150$	−88.7811	+	108.439i	−0.591874	+	0.722924i
$151$	99.7733	−	172.812i	0.660750	−	1.14445i	−0.319668	−	0.947529i	$-0.603572\pi$
$151$	99.7733	−	172.812i	0.660750	−	1.14445i	0.980419	−	0.196924i	$-0.0630951\pi$
$152$	−30.1456	−	20.1805i	−0.198326	−	0.132767i
$153$	5.63925	+	82.3538i	0.0368578	+	0.538260i
$154$	−135.121	+	45.8236i	−0.877406	+	0.297556i
$155$	−15.1364	+	26.2170i	−0.0976542	+	0.169142i
$156$	43.9894	+	264.988i	0.281983	+	1.69864i
$157$	193.810	−	111.896i	1.23446	−	0.712716i	0.266504	−	0.963834i	$-0.414131\pi$
$157$	193.810	−	111.896i	1.23446	−	0.712716i	0.967957	+	0.251118i	$0.0807982\pi$
$158$	−1.67552	−	1.47025i	−0.0106045	−	0.00930536i
$159$	2.49484	+	72.9531i	0.0156908	+	0.458824i
$160$	199.436	+	98.7100i	1.24647	+	0.616937i
$161$			14.2876i			0.0887429i
$162$	−9.69810	+	161.709i	−0.0598648	+	0.998206i
$163$			143.924i			0.882972i	0.897268	+	0.441486i	$0.145549\pi$
$163$			143.924i			0.882972i	−0.897268	+	0.441486i	$0.854451\pi$
$164$	−277.974	+	36.4323i	−1.69496	+	0.222148i
$165$	−11.0803	−	324.006i	−0.0671535	−	1.96367i
$166$	119.888	+	105.200i	0.722217	+	0.633737i
$167$	232.808	−	134.412i	1.39406	−	0.804863i	0.400301	−	0.916384i	$-0.368906\pi$
$167$	232.808	−	134.412i	1.39406	−	0.804863i	0.993762	+	0.111521i	$0.0355723\pi$
$168$	−97.1363	+	51.9943i	−0.578192	+	0.309490i
$169$	166.033	−	287.577i	0.982443	−	1.70164i
$170$	−40.9684	−	120.804i	−0.240990	−	0.710610i
$171$	2.78807	+	40.7161i	0.0163045	+	0.238106i
$172$	−145.355	−	189.657i	−0.845084	−	1.10266i
$173$	−68.3117	+	118.319i	−0.394865	+	0.683926i	−0.993084	−	0.117406i	$-0.962542\pi$
$173$	−68.3117	+	118.319i	−0.394865	+	0.683926i	0.598219	+	0.801333i	$0.295875\pi$
$174$	48.8683	−	59.6885i	0.280852	−	0.343037i
$175$	53.6141	+	92.8623i	0.306366	+	0.530642i
$176$	−240.243	+	64.0750i	−1.36502	+	0.364062i
$177$	−105.660	+	65.9177i	−0.596949	+	0.372416i
$178$	20.9101	+	4.16558i	0.117473	+	0.0234021i
$179$	−78.4371			−0.438196			−0.219098	−	0.975703i	$-0.570311\pi$
$179$	−78.4371			−0.438196			−0.219098	+	0.975703i	$0.570311\pi$
$180$	−49.4140	−	245.418i	−0.274522	−	1.36343i
$181$			237.123i			1.31007i	0.755597	+	0.655037i	$0.227347\pi$
$181$			237.123i			1.31007i	−0.755597	+	0.655037i	$0.772653\pi$
$182$	201.560	+	40.1534i	1.10747	+	0.220623i
$183$	−56.3861	+	105.862i	−0.308121	+	0.578483i
$184$	−1.65001	+	24.8437i	−0.00896742	+	0.135020i
$185$	−138.739	+	80.1008i	−0.749938	+	0.432977i
$186$	−9.22932	−	24.4349i	−0.0496200	−	0.131371i
$187$	123.436	+	71.2656i	0.660083	+	0.381099i
$188$	−90.2416	−	117.746i	−0.480009	−	0.626310i
$189$	113.123	+	50.6596i	0.598536	+	0.268040i
$190$	−20.2550	−	59.7260i	−0.106605	−	0.314347i
$191$	−220.726	−	127.436i	−1.15563	−	0.667205i	−0.205379	−	0.978682i	$-0.565843\pi$
$191$	−220.726	−	127.436i	−1.15563	−	0.667205i	−0.950254	+	0.311477i	$0.899176\pi$
$192$	−174.908	+	79.1913i	−0.910978	+	0.412455i
$193$	147.201	+	254.960i	0.762699	+	1.32103i	0.941454	+	0.337140i	$0.109460\pi$
$193$	147.201	+	254.960i	0.762699	+	1.32103i	−0.178755	+	0.983894i	$0.557207\pi$
$194$	−218.362	−	191.610i	−1.12558	−	0.987680i
$195$	−219.533	+	412.164i	−1.12581	+	2.11366i
$196$	−14.5160	−	110.755i	−0.0740610	−	0.565077i
$197$	212.853			1.08047			0.540237	−	0.841513i	$-0.318335\pi$
$197$	212.853			1.08047			0.540237	+	0.841513i	$0.318335\pi$
$198$	222.365	+	169.699i	1.12305	+	0.857067i
$199$	−206.128			−1.03582			−0.517909	−	0.855435i	$-0.673290\pi$
$199$	−206.128			−1.03582			−0.517909	+	0.855435i	$0.673290\pi$
$200$	82.5014	+	167.663i	0.412507	+	0.838315i
$201$	44.6330	+	71.5426i	0.222055	+	0.355933i
$202$	143.667	+	126.066i	0.711224	+	0.624091i
$203$	−29.5111	−	51.1147i	−0.145375	−	0.251796i
$204$	103.042	+	38.6787i	0.505108	+	0.189601i
$205$	−422.091	−	243.695i	−2.05898	−	1.18875i
$206$	194.349	−	65.9099i	0.943442	−	0.319951i
$207$	23.2445	−	15.6298i	0.112292	−	0.0755065i
$208$	345.841	+	93.0970i	1.66270	+	0.447582i
$209$	61.0272	+	35.2341i	0.291996	+	0.168584i
$210$	−189.019	−	30.9800i	−0.900092	−	0.147524i
$211$	7.29372	−	4.21103i	0.0345674	−	0.0199575i	−0.482617	−	0.875832i	$-0.660314\pi$
$211$	7.29372	−	4.21103i	0.0345674	−	0.0199575i	0.517184	+	0.855874i	$0.326980\pi$
$212$	89.8974	+	37.2977i	0.424044	+	0.175933i
$213$	179.340	−	6.13304i	0.841970	−	0.0287936i
$214$	9.09518	−	45.6555i	0.0425008	−	0.213343i
$215$		−	415.415i		−	1.93216i
$216$	190.851	+	101.152i	0.883571	+	0.468298i
$217$	−19.9847			−0.0920954
$218$	−163.833	−	32.6377i	−0.751526	−	0.149714i
$219$	5.52537	+	161.571i	0.0252300	+	0.737765i
$220$	−399.261	−	165.650i	−1.81482	−	0.752956i
$221$	−102.654	−	177.801i	−0.464496	−	0.804530i
$222$	22.3565	−	136.404i	0.100705	−	0.614435i
$223$	−217.164	+	376.140i	−0.973831	+	1.68672i	−0.290091	+	0.956999i	$0.593686\pi$
$223$	−217.164	+	376.140i	−0.973831	+	1.68672i	−0.683740	+	0.729726i	$0.739648\pi$
$224$	9.39571	+	146.601i	0.0419451	+	0.654470i
$225$	92.4270	−	188.811i	0.410787	−	0.839160i
$226$	17.0147	+	50.1714i	0.0752862	+	0.221997i
$227$	29.4669	−	51.0382i	0.129810	−	0.224838i	−0.793793	−	0.608188i	$-0.791897\pi$
$227$	29.4669	−	51.0382i	0.129810	−	0.224838i	0.923603	+	0.383351i	$0.125230\pi$
$228$	50.9445	+	19.1229i	0.223441	+	0.0838725i
$229$	150.597	−	86.9472i	0.657628	−	0.379682i	−0.133744	−	0.991016i	$-0.542700\pi$
$229$	150.597	−	86.9472i	0.657628	−	0.379682i	0.791373	+	0.611334i	$0.209367\pi$
$230$	−28.5497	+	32.5357i	−0.124129	+	0.141459i
$231$	181.580	−	113.282i	0.786061	−	0.490397i
$232$	−45.4117	−	92.2877i	−0.195740	−	0.397792i
$233$			124.652i			0.534987i	0.963560	+	0.267494i	$0.0861954\pi$
$233$			124.652i			0.534987i	−0.963560	+	0.267494i	$0.913805\pi$
$234$	−155.170	−	371.844i	−0.663118	−	1.58908i
$235$		−	257.906i		−	1.09747i
$236$	21.5783	+	164.640i	0.0914334	+	0.697626i
$237$	2.95116	+	1.57189i	0.0124522	+	0.00663246i
$238$	55.5420	−	63.2965i	0.233370	−	0.265952i
$239$	−111.522	+	64.3874i	−0.466621	+	0.269404i	−0.714824	−	0.699304i	$-0.753493\pi$
$239$	−111.522	+	64.3874i	−0.466621	+	0.269404i	0.248203	+	0.968708i	$0.420160\pi$
$240$	−325.094	−	75.6978i	−1.35456	−	0.315407i
$241$	131.126	−	227.117i	0.544092	−	0.942395i	−0.454571	−	0.890710i	$-0.650208\pi$
$241$	131.126	−	227.117i	0.544092	−	0.942395i	0.998663	−	0.0516849i	$-0.0164591\pi$
$242$	228.221	−	77.3969i	0.943061	−	0.319822i
$243$	−41.3323	−	239.459i	−0.170092	−	0.985428i
$244$	97.2818	+	126.932i	0.398696	+	0.520214i
$245$	97.0968	−	168.177i	0.396314	−	0.686435i
$246$	393.400	−	148.591i	1.59919	−	0.604029i
$247$	−50.7525	−	87.9059i	−0.205476	−	0.355894i
$248$	−34.7499	−	2.30793i	−0.140121	−	0.00930619i
$249$	−211.164	−	112.474i	−0.848048	−	0.451701i
$250$	4.46244	−	22.4003i	0.0178498	−	0.0896013i
$251$	227.156			0.905005			0.452503	−	0.891763i	$-0.350531\pi$
$251$	227.156			0.905005			0.452503	+	0.891763i	$0.350531\pi$
$252$	123.997	−	109.257i	0.492053	−	0.433560i
$253$		−	48.3654i		−	0.191167i
$254$	4.17369	−	20.9509i	0.0164319	−	0.0824838i
$255$	101.279	+	162.341i	0.397172	+	0.636630i
$256$	−0.592754	+	255.999i	−0.00231545	+	0.999997i
$257$	15.0254	−	8.67493i	0.0584647	−	0.0337546i	−0.470483	−	0.882409i	$-0.655920\pi$
$257$	15.0254	−	8.67493i	0.0584647	−	0.0337546i	0.528947	+	0.848655i	$0.322587\pi$
$258$	277.334	+	227.059i	1.07494	+	0.880074i
$259$	−91.5888	−	52.8788i	−0.353625	−	0.204165i
$260$	378.756	+	494.197i	1.45675	+	1.90076i
$261$	−50.8751	+	103.928i	−0.194924	+	0.398192i
$262$	−453.978	+	153.958i	−1.73274	+	0.587626i
$263$	40.5408	+	23.4062i	0.154147	+	0.0889970i	0.575090	−	0.818090i	$-0.304967\pi$
$263$	40.5408	+	23.4062i	0.154147	+	0.0889970i	−0.420942	+	0.907087i	$0.638301\pi$
$264$	328.819	−	176.007i	1.24553	−	0.666695i
$265$	84.6017	+	146.534i	0.319252	+	0.552960i
$266$	27.4602	−	31.2941i	0.103234	−	0.117647i
$267$	−31.9628	+	1.09306i	−0.119711	+	0.00409386i
$268$	111.478	−	14.6107i	0.415962	−	0.0545175i
$269$	−474.565			−1.76418			−0.882091	−	0.471079i	$-0.843865\pi$
$269$	−474.565			−1.76418			−0.882091	+	0.471079i	$0.843865\pi$
$270$	156.375	+	341.406i	0.579167	+	1.26447i
$271$	10.2990			0.0380036			0.0190018	−	0.999819i	$-0.493951\pi$
$271$	10.2990			0.0380036			0.0190018	+	0.999819i	$0.493951\pi$
$272$	103.888	−	103.647i	0.381940	−	0.381057i
$273$	−308.101	+	10.5364i	−1.12857	+	0.0385949i
$274$	−167.372	+	190.740i	−0.610846	+	0.696130i
$275$	−181.490	−	314.351i	−0.659965	−	1.14309i
$276$	−6.11621	−	36.8434i	−0.0221602	−	0.133491i
$277$	333.475	+	192.532i	1.20388	+	0.695060i	0.961416	−	0.275100i	$-0.0887110\pi$
$277$	333.475	+	192.532i	1.20388	+	0.695060i	0.242464	+	0.970160i	$0.422044\pi$
$278$	−97.6249	−	287.868i	−0.351169	−	1.03549i
$279$	21.8621	+	32.5131i	0.0783589	+	0.116534i
$280$	−142.070	+	212.224i	−0.507394	+	0.757944i
$281$	9.19798	+	5.31046i	0.0327330	+	0.0188984i	0.516277	−	0.856422i	$-0.327317\pi$
$281$	9.19798	+	5.31046i	0.0327330	+	0.0188984i	−0.483544	+	0.875320i	$0.660651\pi$
$282$	172.179	+	140.967i	0.610565	+	0.499883i
$283$	−326.705	+	188.623i	−1.15443	+	0.666512i	−0.949964	−	0.312360i	$-0.898880\pi$
$283$	−326.705	+	188.623i	−1.15443	+	0.666512i	−0.204470	+	0.978873i	$0.565547\pi$
$284$	91.6884	−	220.994i	0.322847	−	0.778146i
$285$	50.0728	+	80.2621i	0.175694	+	0.281621i
$286$	−682.306	−	135.924i	−2.38569	−	0.475260i
$287$		−	321.752i		−	1.12109i
$288$	228.227	−	175.659i	0.792456	−	0.609929i
$289$	204.877			0.708918
$290$	34.9355	−	175.367i	0.120467	−	0.604715i
$291$	384.610	+	204.857i	1.32168	+	0.703977i
$292$	199.098	+	82.6040i	0.681841	+	0.282890i
$293$	−124.349	−	215.379i	−0.424399	−	0.735080i	0.571965	−	0.820278i	$-0.306181\pi$
$293$	−124.349	−	215.379i	−0.424399	−	0.735080i	−0.996364	+	0.0851974i	$0.972848\pi$
$294$	59.2042	+	156.745i	0.201375	+	0.533146i
$295$	−144.336	+	249.998i	−0.489276	+	0.847451i
$296$	−153.150	−	102.524i	−0.517400	−	0.346366i
$297$	−382.937	−	171.489i	−1.28935	−	0.577405i
$298$	−185.709	+	62.9797i	−0.623184	+	0.211341i
$299$	−34.8336	+	60.3336i	−0.116500	+	0.201785i
$300$	−178.007	−	216.513i	−0.593356	−	0.721709i
$301$	237.497	−	137.119i	0.789026	−	0.455544i
$302$	299.978	+	263.227i	0.993305	+	0.871613i
$303$	−253.047	−	134.782i	−0.835140	−	0.444825i
$304$	51.3626	−	51.2438i	0.168956	−	0.168565i
$305$			278.026i			0.911561i
$306$	−163.737	−	21.1185i	−0.535088	−	0.0690146i
$307$		−	557.648i		−	1.81644i	−0.418488	−	0.908222i	$-0.637440\pi$
$307$		−	557.648i		−	1.81644i	0.418488	−	0.908222i	$-0.362560\pi$
$308$	−37.0830	−	282.939i	−0.120399	−	0.918632i
$309$	−261.174	+	162.937i	−0.845222	+	0.527305i
$310$	−45.5090	−	39.9337i	−0.146803	−	0.128818i
$311$	−124.423	+	71.8354i	−0.400072	+	0.230982i	−0.686515	−	0.727115i	$-0.740860\pi$
$311$	−124.423	+	71.8354i	−0.400072	+	0.230982i	0.286443	+	0.958097i	$0.407527\pi$
$312$	−536.951	−	17.2601i	−1.72100	−	0.0553207i
$313$	−135.455	+	234.614i	−0.432763	+	0.749567i	−0.997110	−	0.0759706i	$-0.975794\pi$
$313$	−135.455	+	234.614i	−0.432763	+	0.749567i	0.564347	+	0.825537i	$0.309128\pi$
$314$	143.749	+	423.874i	0.457799	+	1.34992i
$315$	286.641	−	19.6280i	0.909970	−	0.0623110i
$316$	3.53853	−	2.71196i	0.0111979	−	0.00858214i
$317$	−152.700	+	264.483i	−0.481702	+	0.834332i	−0.999779	−	0.0210014i	$-0.993315\pi$
$317$	−152.700	+	264.483i	−0.481702	+	0.834332i	0.518077	+	0.855334i	$0.326648\pi$
$318$	−144.069	−	23.6128i	−0.453048	−	0.0742540i
$319$	99.8988	+	173.030i	0.313162	+	0.542413i
$320$	−271.545	+	352.614i	−0.848577	+	1.10192i
$321$	2.38661	+	69.7881i	0.00743492	+	0.217409i
$322$	−28.0245	−	5.58286i	−0.0870327	−	0.0173381i
$323$	−41.5908			−0.128764
$324$	−313.397	−	82.2101i	−0.967274	−	0.253735i
$325$			522.851i			1.60877i
$326$	−282.302	−	56.2383i	−0.865956	−	0.172510i
$327$	250.432	−	8.56424i	0.765846	−	0.0261903i
$328$	37.1575	−	559.471i	0.113285	−	1.70570i
$329$	147.447	−	85.1286i	0.448167	−	0.258750i
$330$	639.854	+	104.871i	1.93895	+	0.317792i
$331$	371.718	+	214.612i	1.12302	+	0.648373i	0.942169	−	0.335138i	$-0.108783\pi$
$331$	371.718	+	214.612i	1.12302	+	0.648373i	0.180846	+	0.983511i	$0.442116\pi$
$332$	−253.192	+	194.048i	−0.762627	+	0.584483i
$333$	14.1644	+	206.852i	0.0425357	+	0.621178i
$334$	172.674	+	509.165i	0.516988	+	1.52445i
$335$	169.274	+	97.7305i	0.505296	+	0.291733i
$336$	−64.0288	−	210.845i	−0.190562	−	0.627516i
$337$	−233.725	−	404.823i	−0.693545	−	1.20125i	−0.970669	−	0.240421i	$-0.922715\pi$
$337$	−233.725	−	404.823i	−0.693545	−	1.20125i	0.277124	−	0.960834i	$-0.410619\pi$
$338$	499.194	+	438.037i	1.47690	+	1.29597i
$339$	−42.0624	−	67.4222i	−0.124078	−	0.198886i
$340$	252.960	−	33.1538i	0.743999	−	0.0975113i
$341$	67.6507			0.198389
$342$	−80.9524	−	10.4411i	−0.236703	−	0.0305295i
$343$	353.141			1.02957
$344$	428.801	−	210.999i	1.24651	−	0.613368i
$345$	30.5235	−	57.3065i	0.0884739	−	0.166106i
$346$	−205.386	−	180.224i	−0.593600	−	0.520877i
$347$	111.555	+	193.219i	0.321484	+	0.556826i	0.980794	−	0.195045i	$-0.0624851\pi$
$347$	111.555	+	193.219i	0.321484	+	0.556826i	−0.659311	+	0.751871i	$0.729152\pi$
$348$	97.9812	+	119.176i	0.281555	+	0.342460i
$349$	−42.4023	−	24.4810i	−0.121497	−	0.0701461i	0.438020	−	0.898965i	$-0.355680\pi$
$349$	−42.4023	−	24.4810i	−0.121497	−	0.0701461i	−0.559517	+	0.828819i	$0.689013\pi$
$350$	−203.095	+	68.8759i	−0.580272	+	0.196788i
$351$	354.187	+	489.723i	1.00908	+	1.39522i
$352$	−31.8057	−	496.264i	−0.0903570	−	1.40984i
$353$	32.8296	+	18.9542i	0.0930017	+	0.0536945i	0.545780	−	0.837929i	$-0.316234\pi$
$353$	32.8296	+	18.9542i	0.0930017	+	0.0536945i	−0.452778	+	0.891623i	$0.649567\pi$
$354$	−88.0082	−	233.005i	−0.248611	−	0.658206i
$355$	360.224	−	207.975i	1.01471	−	0.585846i
$356$	−16.3412	+	39.3866i	−0.0459022	+	0.110637i
$357$	−59.3820	+	111.487i	−0.166336	+	0.312288i
$358$	30.6492	−	153.851i	0.0856122	−	0.429752i
$359$		−	538.228i		−	1.49924i	−0.661868	−	0.749621i	$-0.730236\pi$
$359$		−	538.228i		−	1.49924i	0.661868	−	0.749621i	$-0.269764\pi$
$360$	500.685	−	1.02692i	1.39079	−	0.00285255i
$361$	340.437			0.943040
$362$	−465.107	−	92.6555i	−1.28483	−	0.255955i
$363$	−306.692	+	191.335i	−0.844881	+	0.527092i
$364$	−157.518	+	379.661i	−0.432743	+	1.04303i
$365$	187.369	+	324.533i	0.513340	+	0.889130i
$366$	−185.612	−	151.965i	−0.507136	−	0.415204i
$367$	58.2868	−	100.956i	0.158820	−	0.275084i	−0.775624	−	0.631196i	$-0.782564\pi$
$367$	58.2868	−	100.956i	0.158820	−	0.275084i	0.934443	+	0.356112i	$0.115898\pi$
$368$	−48.0851	−	12.9440i	−0.130666	−	0.0351740i
$369$	−523.458	+	351.978i	−1.41859	+	0.953871i
$370$	−102.902	−	303.429i	−0.278114	−	0.820079i
$371$	−55.8501	+	96.7352i	−0.150539	+	0.260742i
$372$	51.5345	−	8.55501i	0.138533	−	0.0229973i
$373$	−117.381	+	67.7702i	−0.314695	+	0.181689i	−0.649026	−	0.760767i	$-0.724823\pi$
$373$	−117.381	+	67.7702i	−0.314695	+	0.181689i	0.334330	+	0.942456i	$0.391490\pi$
$374$	−188.017	+	214.267i	−0.502718	+	0.572906i
$375$	1.17096	+	34.2407i	0.00312256	+	0.0913086i
$376$	266.216	−	130.996i	0.708021	−	0.348394i
$377$		−	287.796i		−	0.763384i
$378$	−143.569	+	202.091i	−0.379813	+	0.534633i
$379$		−	292.521i		−	0.771822i	−0.922536	−	0.385911i	$-0.873887\pi$
$379$		−	292.521i		−	0.771822i	0.922536	−	0.385911i	$-0.126113\pi$
$380$	125.065	−	16.3914i	0.329117	−	0.0431353i
$381$	1.09519	+	32.0251i	0.00287452	+	0.0840554i
$382$	336.209	−	383.149i	0.880128	−	1.00301i
$383$	230.166	−	132.886i	0.600956	−	0.346962i	−0.168462	−	0.985708i	$-0.553880\pi$
$383$	230.166	−	132.886i	0.600956	−	0.346962i	0.769417	+	0.638746i	$0.220547\pi$
$384$	−86.9855	−	374.018i	−0.226525	−	0.974005i
$385$	248.047	−	429.630i	0.644278	−	1.11592i
$386$	−557.611	+	189.103i	−1.44459	+	0.489905i
$387$	−482.887	−	236.384i	−1.24777	−	0.610810i
$388$	461.159	−	353.436i	1.18855	−	0.910918i
$389$	−70.7571	+	122.555i	−0.181895	+	0.315051i	−0.942526	−	0.334133i	$-0.891556\pi$
$389$	−70.7571	+	122.555i	−0.181895	+	0.315051i	0.760631	+	0.649185i	$0.224890\pi$
$390$	−722.659	−	591.657i	−1.85297	−	1.51707i
$391$	14.2728	+	24.7212i	0.0365033	+	0.0632255i
$392$	222.913	+	14.8049i	0.568657	+	0.0377676i
$393$	610.072	−	380.603i	1.55235	−	0.968456i
$394$	−83.1721	+	417.503i	−0.211097	+	1.05965i
$395$	7.75062			0.0196218
$396$	−419.747	+	369.849i	−1.05997	+	0.933963i
$397$		−	371.596i		−	0.936009i	−0.883726	−	0.468004i	$-0.844973\pi$
$397$		−	371.596i		−	0.936009i	0.883726	−	0.468004i	$-0.155027\pi$
$398$	80.5442	−	404.311i	0.202372	−	1.01586i
$399$	−29.3588	+	55.1197i	−0.0735808	+	0.138145i
$400$	−361.101	+	96.3088i	−0.902753	+	0.240772i
$401$	−25.8599	+	14.9302i	−0.0644885	+	0.0372325i	−0.531898	−	0.846809i	$-0.678521\pi$
$401$	−25.8599	+	14.9302i	−0.0644885	+	0.0372325i	0.467409	+	0.884041i	$0.345188\pi$
$402$	−157.768	+	59.5905i	−0.392458	+	0.148235i
$403$	−84.3913	−	48.7233i	−0.209408	−	0.120902i
$404$	−303.411	+	232.537i	−0.751018	+	0.575586i
$405$	−345.501	−	444.864i	−0.853090	−	1.09843i
$406$	111.791	−	37.9117i	0.275347	−	0.0933787i
$407$	310.040	+	179.001i	0.761768	+	0.439807i
$408$	−116.130	+	186.999i	−0.284632	+	0.458330i
$409$	180.690	+	312.965i	0.441785	+	0.765195i	0.997822	−	0.0659631i	$-0.0210120\pi$
$409$	180.690	+	312.965i	0.441785	+	0.765195i	−0.556037	+	0.831158i	$0.687679\pi$
$410$	642.928	−	732.691i	1.56812	−	1.78705i
$411$	178.943	−	335.958i	0.435385	−	0.817417i
$412$	53.3379	+	406.962i	0.129461	+	0.987771i
$413$	−190.568			−0.461425
$414$	21.5745	+	51.7005i	0.0521123	+	0.124880i
$415$	−554.579			−1.33634
$416$	−317.742	+	641.974i	−0.763804	+	1.54321i
$417$	241.341	+	386.847i	0.578755	+	0.927691i
$418$	−92.9564	+	105.935i	−0.222384	+	0.253432i
$419$	−98.1870	−	170.065i	−0.234336	−	0.405883i	0.724743	−	0.689019i	$-0.241958\pi$
$419$	−98.1870	−	170.065i	−0.234336	−	0.405883i	−0.959080	+	0.283136i	$0.908625\pi$
$420$	134.625	−	358.648i	0.320536	−	0.853923i
$421$	−82.7053	−	47.7499i	−0.196450	−	0.113420i	0.398549	−	0.917147i	$-0.369514\pi$
$421$	−82.7053	−	47.7499i	−0.196450	−	0.113420i	−0.594998	+	0.803727i	$0.702847\pi$
$422$	5.40975	+	15.9518i	0.0128193	+	0.0378004i
$423$	−299.795	−	146.756i	−0.708735	−	0.346941i
$424$	−108.285	+	161.756i	−0.255389	+	0.381500i
$425$	185.532	+	107.117i	0.436545	+	0.252040i
$426$	−58.0469	+	354.163i	−0.136260	+	0.831369i
$427$	−158.950	+	91.7699i	−0.372249	+	0.214918i
$428$	85.9974	+	35.6796i	0.200928	+	0.0833636i
$429$	1042.96	−	35.6671i	2.43114	−	0.0831400i
$430$	814.819	+	162.323i	1.89493	+	0.377495i
$431$			237.261i			0.550490i	0.961374	+	0.275245i	$0.0887589\pi$
$431$			237.261i			0.550490i	−0.961374	+	0.275245i	$0.911241\pi$
$432$	−272.981	+	334.822i	−0.631900	+	0.775050i
$433$	−180.685			−0.417287			−0.208644	−	0.977992i	$-0.566905\pi$
$433$	−180.685			−0.417287			−0.208644	+	0.977992i	$0.566905\pi$
$434$	7.80899	−	39.1991i	0.0179931	−	0.0903206i
$435$	9.16721	+	268.063i	0.0210740	+	0.616238i
$436$	128.035	−	308.598i	0.293658	−	0.707793i
$437$	7.05653	+	12.2223i	0.0161477	+	0.0279686i
$438$	−319.073	−	52.2956i	−0.728477	−	0.119396i
$439$	93.0216	−	161.118i	0.211894	−	0.367012i	−0.740413	−	0.672152i	$-0.765370\pi$
$439$	93.0216	−	161.118i	0.211894	−	0.367012i	0.952307	+	0.305140i	$0.0987034\pi$
$440$	480.927	−	718.406i	1.09301	−	1.63274i
$441$	−140.241	−	208.565i	−0.318007	−	0.472936i
$442$	388.861	−	131.875i	0.879777	−	0.298360i
$443$	141.006	−	244.230i	0.318299	−	0.551310i	−0.661834	−	0.749650i	$-0.730222\pi$
$443$	141.006	−	244.230i	0.318299	−	0.551310i	0.980133	+	0.198340i	$0.0635551\pi$
$444$	258.816	+	97.1512i	0.582919	+	0.218809i
$445$	−64.2009	+	37.0664i	−0.144272	+	0.0832954i
$446$	−652.925	−	572.935i	−1.46396	−	1.28461i
$447$	249.563	−	155.694i	0.558306	−	0.348308i
$448$	−291.224	−	38.8549i	−0.650053	−	0.0867298i
$449$			158.722i			0.353502i	0.984256	+	0.176751i	$0.0565588\pi$
$449$			158.722i			0.353502i	−0.984256	+	0.176751i	$0.943441\pi$
$450$	334.229	+	255.069i	0.742731	+	0.566820i
$451$			1089.17i			2.41501i
$452$	−105.057	+	13.7692i	−0.232428	+	0.0304629i
$453$	−528.365	−	281.426i	−1.16637	−	0.621249i
$454$	88.5950	+	77.7411i	0.195143	+	0.171236i
$455$	−618.855	+	357.296i	−1.36012	+	0.785266i
$456$	−57.4153	+	92.4532i	−0.125911	+	0.202748i
$457$	−213.180	+	369.239i	−0.466477	+	0.807963i	−0.999267	−	0.0382852i	$-0.987810\pi$
$457$	−213.180	+	369.239i	−0.466477	+	0.807963i	0.532789	+	0.846248i	$0.321144\pi$
$458$	111.698	+	329.364i	0.243881	+	0.719135i
$459$	246.339	−	25.3519i	0.536686	−	0.0552329i
$460$	−52.6616	−	68.7122i	−0.114482	−	0.149374i
$461$	−203.028	+	351.655i	−0.440408	+	0.762808i	−0.997720	−	0.0674949i	$-0.978499\pi$
$461$	−203.028	+	351.655i	−0.440408	+	0.762808i	0.557312	+	0.830303i	$0.311833\pi$
$462$	151.245	+	400.426i	0.327370	+	0.866724i
$463$	−357.640	−	619.450i	−0.772440	−	1.33790i	−0.936222	−	0.351408i	$-0.885703\pi$
$463$	−357.640	−	619.450i	−0.772440	−	1.33790i	0.163783	−	0.986496i	$-0.447630\pi$
$464$	198.763	−	53.0118i	0.428368	−	0.114250i
$465$	80.1571	+	42.6945i	0.172381	+	0.0918162i
$466$	−244.500	−	48.7076i	−0.524677	−	0.104523i
$467$	419.019			0.897256			0.448628	−	0.893719i	$-0.351913\pi$
$467$	419.019			0.897256			0.448628	+	0.893719i	$0.351913\pi$
$468$	789.988	−	159.061i	1.68801	−	0.339875i
$469$			129.034i			0.275126i
$470$	505.871	+	100.776i	1.07632	+	0.214417i
$471$	−355.365	−	569.618i	−0.754491	−	1.20938i
$472$	−331.365	−	22.0078i	−0.702045	−	0.0466267i
$473$	−803.957	+	464.165i	−1.69970	+	0.981321i
$474$	−4.23636	+	5.17436i	−0.00893748	+	0.0109164i
$475$	91.7279	+	52.9591i	0.193111	+	0.111493i
$476$	102.451	+	133.676i	0.215232	+	0.280832i
$477$	218.475	−	14.9603i	0.458020	−	0.0313633i
$478$	−82.7161	−	243.906i	−0.173046	−	0.510263i
$479$	−27.1481	−	15.6740i	−0.0566766	−	0.0327223i	0.471394	−	0.881923i	$-0.343751\pi$
$479$	−27.1481	−	15.6740i	−0.0566766	−	0.0327223i	−0.528071	+	0.849201i	$0.677084\pi$
$480$	275.508	−	608.079i	0.573975	−	1.26683i
$481$	−257.840	−	446.593i	−0.536051	−	0.928467i
$482$	394.244	+	345.944i	0.817933	+	0.717727i
$483$	42.8378	−	1.46496i	0.0886910	−	0.00303305i
$484$	62.6337	+	477.888i	0.129409	+	0.987372i
$485$	1010.10			2.08268
$486$	485.839	+	12.4966i	0.999669	+	0.0257132i
$487$	156.973			0.322327			0.161163	−	0.986928i	$-0.448475\pi$
$487$	156.973			0.322327			0.161163	+	0.986928i	$0.448475\pi$
$488$	−286.985	+	141.216i	−0.588084	+	0.289376i
$489$	431.521	−	14.7571i	0.882457	−	0.0301782i
$490$	291.931	+	256.166i	0.595777	+	0.522788i
$491$	−15.1335	−	26.2120i	−0.0308218	−	0.0533849i	0.850203	−	0.526455i	$-0.176479\pi$
$491$	−15.1335	−	26.2120i	−0.0308218	−	0.0533849i	−0.881025	+	0.473070i	$0.843146\pi$
$492$	137.735	+	829.700i	0.279949	+	1.68638i
$493$	−102.123	−	58.9609i	−0.207147	−	0.119596i
$494$	192.255	−	65.1998i	0.389180	−	0.131983i
$495$	−970.315	+	66.4432i	−1.96023	+	0.134229i
$496$	18.1054	−	67.2587i	0.0365028	−	0.135602i
$497$	237.803	+	137.296i	0.478477	+	0.276249i
$498$	303.124	−	370.240i	0.608683	−	0.743455i
$499$	−92.1565	+	53.2066i	−0.184682	+	0.106626i	−0.589491	−	0.807775i	$-0.700672\pi$
$499$	−92.1565	+	53.2066i	−0.184682	+	0.106626i	0.404808	+	0.914402i	$0.367338\pi$
$500$	42.1936	+	17.5058i	0.0843872	+	0.0350116i
$501$	−426.871	−	684.236i	−0.852039	−	1.36574i
$502$	−88.7609	+	445.557i	−0.176815	+	0.887565i
$503$			895.530i			1.78038i	0.455592	+	0.890189i	$0.349428\pi$
$503$			895.530i			1.78038i	−0.455592	+	0.890189i	$0.650572\pi$
$504$	165.852	+	285.908i	0.329071	+	0.567277i
$505$	−664.577			−1.31599
$506$	94.8666	+	18.8987i	0.187483	+	0.0373492i
$507$	−879.252	−	468.321i	−1.73422	−	0.923710i
$508$	39.4634	+	16.3730i	0.0776839	+	0.0322304i
$509$	−136.924	−	237.160i	−0.269006	−	0.465932i	0.699599	−	0.714535i	$-0.253362\pi$
$509$	−136.924	−	237.160i	−0.269006	−	0.465932i	−0.968605	+	0.248603i	$0.920029\pi$
$510$	−357.999	+	135.220i	−0.701959	+	0.265137i
$511$	−123.692	+	214.241i	−0.242059	+	0.419259i
$512$	−501.900	−	101.194i	−0.980274	−	0.197644i
$513$	121.791	−	12.5341i	0.237410	−	0.0244330i
$514$	11.1444	+	32.8614i	0.0216816	+	0.0639328i
$515$	−356.775	+	617.953i	−0.692768	+	1.19991i
$516$	−553.735	+	455.255i	−1.07313	+	0.882277i
$517$	−499.127	+	288.171i	−0.965430	+	0.557391i
$518$	139.508	−	158.985i	0.269320	−	0.306921i
$519$	361.755	+	192.684i	0.697023	+	0.371259i
$520$	−1117.34	+	549.807i	−2.14874	+	1.05732i
$521$		−	575.650i		−	1.10489i	−0.833548	−	0.552447i	$-0.813694\pi$
$521$		−	575.650i		−	1.10489i	0.833548	−	0.552447i	$-0.186306\pi$
$522$	−183.971	−	140.399i	−0.352436	−	0.268964i
$523$		−	83.4381i		−	0.159537i	−0.996813	−	0.0797687i	$-0.974582\pi$
$523$		−	83.4381i		−	0.159537i	0.996813	−	0.0797687i	$-0.0254182\pi$
$524$	−124.591	−	950.617i	−0.237770	−	1.81415i
$525$	272.927	−	170.270i	0.519861	−	0.324323i
$526$	−61.7515	+	70.3730i	−0.117398	+	0.133789i
$527$	−34.5786	+	19.9639i	−0.0656140	+	0.0378823i
$528$	216.746	+	713.739i	0.410503	+	1.35178i
$529$	−259.657	+	449.739i	−0.490845	+	0.850168i
$530$	−320.479	+	108.685i	−0.604677	+	0.205065i
$531$	208.471	+	310.036i	0.392601	+	0.583872i
$532$	50.6521	+	66.0902i	0.0952107	+	0.124230i
$533$	784.441	−	1358.69i	1.47175	−	2.54914i
$534$	10.3454	−	63.1209i	0.0193735	−	0.118204i
$535$	80.9314	+	140.177i	0.151274	+	0.262014i
$536$	−14.9015	+	224.368i	−0.0278014	+	0.418597i
$537$	8.04245	+	235.174i	0.0149766	+	0.437940i
$538$	185.435	−	930.839i	0.344676	−	1.73018i
$539$	−433.965			−0.805130
$540$	−730.757	+	173.319i	−1.35325	+	0.320961i
$541$		−	995.189i		−	1.83954i	−0.392463	−	0.919768i	$-0.628377\pi$
$541$		−	995.189i		−	1.83954i	0.392463	−	0.919768i	$-0.371623\pi$
$542$	−4.02430	+	20.2010i	−0.00742492	+	0.0372712i
$543$	710.954	−	24.3131i	1.30931	−	0.0447756i
$544$	162.706	+	244.271i	0.299092	+	0.449028i
$545$	503.020	−	290.419i	0.922973	−	0.532879i
$546$	99.7231	−	608.444i	0.182643	−	1.11437i
$547$	−447.270	−	258.231i	−0.817678	−	0.472087i	0.0319370	−	0.999490i	$-0.489832\pi$
$547$	−447.270	−	258.231i	−0.817678	−	0.472087i	−0.849615	+	0.527403i	$0.823166\pi$
$548$	−308.727	−	402.824i	−0.563371	−	0.735080i
$549$	323.183	+	158.205i	0.588676	+	0.288169i
$550$	687.503	−	233.154i	1.25000	−	0.423916i
$551$	−50.4903	−	29.1506i	−0.0916339	−	0.0529049i
$552$	74.6566	+	2.39981i	0.135248	+	0.00434748i
$553$	2.55830	+	4.43111i	0.00462622	+	0.00801285i
$554$	−507.947	+	578.865i	−0.916873	+	1.04488i
$555$	254.387	+	407.760i	0.458355	+	0.734702i
$556$	602.787	−	79.0034i	1.08415	−	0.142092i
$557$	440.448			0.790751			0.395376	−	0.918520i	$-0.370614\pi$
$557$	440.448			0.790751			0.395376	+	0.918520i	$0.370614\pi$
$558$	−72.3157	+	30.1772i	−0.129598	+	0.0540810i
$559$	1337.20			2.39213
$560$	−360.755	−	361.591i	−0.644206	−	0.645699i
$561$	201.016	−	377.398i	0.358316	−	0.672723i
$562$	−14.0103	+	15.9664i	−0.0249294	+	0.0284100i
$563$	129.798	+	224.816i	0.230547	+	0.399319i	0.957969	−	0.286871i	$-0.0926152\pi$
$563$	129.798	+	224.816i	0.230547	+	0.399319i	−0.727422	+	0.686190i	$0.759282\pi$
$564$	−343.780	+	282.640i	−0.609538	+	0.501134i
$565$	−159.525	−	92.1019i	−0.282345	−	0.163012i
$566$	−242.317	−	714.521i	−0.428121	−	1.26241i
$567$	140.291	−	344.366i	0.247427	−	0.607347i
$568$	397.642	+	266.196i	0.700075	+	0.468655i
$569$	−892.111	−	515.060i	−1.56786	−	0.905203i	−0.996419	−	0.0845575i	$-0.973052\pi$
$569$	−892.111	−	515.060i	−1.56786	−	0.905203i	−0.571438	−	0.820645i	$-0.693614\pi$
$570$	−176.997	+	66.8533i	−0.310520	+	0.117287i
$571$	−683.633	+	394.696i	−1.19726	+	0.691236i	−0.959942	−	0.280197i	$-0.909600\pi$
$571$	−683.633	+	394.696i	−1.19726	+	0.691236i	−0.237313	+	0.971433i	$0.576267\pi$
$572$	533.220	−	1285.20i	0.932203	−	2.24686i
$573$	−359.453	+	674.857i	−0.627318	+	1.17776i
$574$	631.102	+	125.724i	1.09948	+	0.219031i
$575$		−	72.6963i		−	0.126428i
$576$	255.369	+	516.297i	0.443349	+	0.896349i
$577$	−100.099			−0.173482			−0.0867411	−	0.996231i	$-0.527645\pi$
$577$	−100.099			−0.173482			−0.0867411	+	0.996231i	$0.527645\pi$
$578$	−80.0554	+	401.858i	−0.138504	+	0.695256i
$579$	749.339	−	467.487i	1.29419	−	0.807404i
$580$	330.325	+	137.049i	0.569526	+	0.236292i
$581$	−183.054	−	317.058i	−0.315067	−	0.545711i
$582$	−552.105	+	674.349i	−0.948633	+	1.15868i
$583$	189.060	−	327.461i	0.324288	−	0.561683i
$584$	−239.821	+	358.244i	−0.410653	+	0.613431i
$585$	1258.28	+	615.954i	2.15090	+	1.05291i
$586$	471.045	−	159.746i	0.803831	−	0.272604i
$587$	−64.4085	+	111.559i	−0.109725	+	0.190049i	−0.915659	−	0.401957i	$-0.868330\pi$
$587$	−64.4085	+	111.559i	−0.109725	+	0.190049i	0.805934	+	0.592005i	$0.201664\pi$
$588$	−330.583	+	54.8786i	−0.562215	+	0.0933309i
$589$	−17.0958	+	9.87028i	−0.0290252	+	0.0167577i
$590$	−433.961	−	380.796i	−0.735528	−	0.645417i
$591$	−21.8247	−	638.187i	−0.0369284	−	1.07984i
$592$	260.940	−	260.337i	0.440777	−	0.439758i
$593$		−	845.625i		−	1.42601i	−0.701158	−	0.713006i	$-0.747333\pi$
$593$		−	845.625i		−	1.42601i	0.701158	−	0.713006i	$-0.252667\pi$
$594$	486.001	−	684.105i	0.818183	−	1.15169i
$595$			292.798i			0.492097i
$596$	−50.9666	−	388.869i	−0.0855145	−	0.652465i
$597$	21.1351	+	618.023i	0.0354021	+	1.03521i
$598$	−104.731	−	91.9000i	−0.175135	−	0.153679i
$599$	−404.246	+	233.391i	−0.674868	+	0.389635i	−0.797919	−	0.602765i	$-0.794066\pi$
$599$	−404.246	+	233.391i	−0.674868	+	0.389635i	0.123051	+	0.992400i	$0.460732\pi$
$600$	494.236	−	264.551i	0.823727	−	0.440918i
$601$	−101.377	+	175.589i	−0.168680	+	0.292162i	−0.937956	−	0.346754i	$-0.887284\pi$
$601$	−101.377	+	175.589i	−0.168680	+	0.292162i	0.769276	+	0.638916i	$0.220617\pi$
$602$	176.151	+	519.419i	0.292610	+	0.862822i
$603$	209.926	−	141.156i	0.348136	−	0.234090i
$604$	−633.525	+	485.538i	−1.04888	+	0.803872i
$605$	−418.955	+	725.652i	−0.692488	+	1.19942i
$606$	363.247	−	443.676i	0.599418	−	0.732138i
$607$	−162.045	−	280.671i	−0.266961	−	0.462390i	0.701115	−	0.713049i	$-0.252686\pi$
$607$	−162.045	−	280.671i	−0.266961	−	0.462390i	−0.968076	+	0.250659i	$0.919353\pi$
$608$	80.4427	+	120.769i	0.132307	+	0.198633i
$609$	−150.229	+	93.7225i	−0.246681	+	0.153896i
$610$	−545.336	−	108.638i	−0.893994	−	0.178095i
$611$	830.185			1.35873
$612$	105.403	−	312.911i	0.172227	−	0.511293i
$613$			901.063i			1.46992i	0.678108	+	0.734962i	$0.262800\pi$
$613$			901.063i			1.46992i	−0.678108	+	0.734962i	$0.737200\pi$
$614$	1093.80	+	217.900i	1.78144	+	0.354886i
$615$	−687.378	+	1290.52i	−1.11769	+	2.09841i
$616$	569.463	+	37.8212i	0.924452	+	0.0613980i
$617$	210.860	−	121.740i	0.341751	−	0.197310i	−0.319295	−	0.947655i	$-0.603446\pi$
$617$	210.860	−	121.740i	0.341751	−	0.197310i	0.661046	+	0.750345i	$0.270113\pi$
$618$	−217.542	−	575.949i	−0.352009	−	0.931956i
$619$	−216.653	−	125.085i	−0.350005	−	0.202075i	0.314683	−	0.949197i	$-0.398102\pi$
$619$	−216.653	−	125.085i	−0.350005	−	0.202075i	−0.664687	+	0.747122i	$0.731435\pi$
$620$	96.1108	−	73.6600i	0.155017	−	0.118806i
$621$	−49.2455	−	68.0902i	−0.0793003	−	0.109646i
$622$	−92.2841	−	272.119i	−0.148367	−	0.437490i
$623$	−42.3825	−	24.4695i	−0.0680297	−	0.0392769i
$624$	243.667	−	1046.46i	0.390493	−	1.67702i
$625$	331.680	+	574.486i	0.530688	+	0.919178i
$626$	−407.258	−	357.364i	−0.650571	−	0.570869i
$627$	99.3831	−	186.587i	0.158506	−	0.297587i
$628$	−887.581	+	116.330i	−1.41334	+	0.185238i
$629$	−211.296			−0.335923
$630$	−73.5049	+	569.903i	−0.116674	+	0.904608i
$631$	−839.956			−1.33115			−0.665575	−	0.746331i	$-0.731814\pi$
$631$	−839.956			−1.33115			−0.665575	+	0.746331i	$0.731814\pi$
$632$	3.93671	+	8.00037i	0.00622898	+	0.0126588i
$633$	−13.3736	−	21.4366i	−0.0211273	−	0.0338651i
$634$	−459.106	−	402.860i	−0.724142	−	0.635426i
$635$	37.1387	+	64.3261i	0.0584861	+	0.101301i
$636$	102.610	−	273.359i	0.161337	−	0.429810i
$637$	541.352	+	312.550i	0.849847	+	0.490659i
$638$	−378.426	+	128.336i	−0.593144	+	0.201154i
$639$	−36.7767	−	537.075i	−0.0575535	−	0.840494i
$640$	−585.532	−	670.407i	−0.914894	−	1.04751i
$641$	807.530	+	466.228i	1.25980	+	0.727344i	0.973035	−	0.230658i	$-0.0740878\pi$
$641$	807.530	+	466.228i	1.25980	+	0.727344i	0.286762	+	0.958002i	$0.407421\pi$
$642$	−137.819	−	22.5884i	−0.214671	−	0.0351844i
$643$	137.674	−	79.4863i	0.214112	−	0.123618i	−0.389109	−	0.921192i	$-0.627217\pi$
$643$	137.674	−	79.4863i	0.214112	−	0.123618i	0.603221	+	0.797574i	$0.293884\pi$
$644$	21.9011	−	52.7874i	0.0340079	−	0.0819681i
$645$	−1245.52	+	42.5941i	−1.93103	+	0.0660373i
$646$	16.2515	−	81.5785i	0.0251571	−	0.126283i
$647$			169.902i			0.262600i	0.991343	+	0.131300i	$0.0419152\pi$
$647$			169.902i			0.262600i	−0.991343	+	0.131300i	$0.958085\pi$
$648$	283.711	−	582.591i	0.437825	−	0.899060i
$649$	645.098			0.993988
$650$	−1025.55	−	204.303i	−1.57777	−	0.314313i
$651$	2.04911	+	59.9191i	0.00314763	+	0.0920416i
$652$	220.618	−	531.748i	0.338371	−	0.815564i
$653$	93.3433	+	161.675i	0.142945	+	0.247589i	0.928605	−	0.371071i	$-0.121009\pi$
$653$	93.3433	+	161.675i	0.142945	+	0.247589i	−0.785659	+	0.618660i	$0.787676\pi$
$654$	−81.0574	+	494.558i	−0.123941	+	0.756204i
$655$	833.387	−	1443.47i	1.27235	−	2.20377i
$656$	1082.86	+	291.495i	1.65070	+	0.444352i
$657$	483.862	−	33.1329i	0.736472	−	0.0504306i
$658$	109.361	+	322.475i	0.166203	+	0.490084i
$659$	47.0020	−	81.4099i	0.0713232	−	0.123535i	−0.828158	−	0.560494i	$-0.810611\pi$
$659$	47.0020	−	81.4099i	0.0713232	−	0.123535i	0.899481	+	0.436959i	$0.143944\pi$
$660$	−455.723	+	1214.07i	−0.690489	+	1.83950i
$661$	307.644	−	177.619i	0.465423	−	0.268712i	−0.248899	−	0.968529i	$-0.580069\pi$
$661$	307.644	−	177.619i	0.465423	−	0.268712i	0.714322	+	0.699817i	$0.246735\pi$
$662$	−566.200	+	645.250i	−0.855287	+	0.974698i
$663$	−522.567	+	326.011i	−0.788185	+	0.491722i
$664$	−281.683	−	572.449i	−0.424222	−	0.862123i
$665$			144.761i			0.217685i
$666$	−411.267	−	53.0443i	−0.617518	−	0.0796461i
$667$			40.0146i			0.0599919i
$668$	−1066.18	+	139.737i	−1.59608	+	0.209187i
$669$	1150.03	+	612.545i	1.71902	+	0.915613i
$670$	−257.838	+	293.836i	−0.384833	+	0.438561i
$671$	538.067	−	310.653i	0.801888	−	0.462970i
$672$	438.584	−	43.2022i	0.652654	−	0.0642891i
$673$	−371.462	+	643.391i	−0.551949	+	0.956004i	0.446185	+	0.894941i	$0.352782\pi$
$673$	−371.462	+	643.391i	−0.551949	+	0.956004i	−0.998134	+	0.0610631i	$0.980551\pi$
$674$	885.370	−	300.257i	1.31361	−	0.445485i
$675$	−575.579	−	257.759i	−0.852709	−	0.381866i
$676$	−1054.25	+	807.985i	−1.55954	+	1.19524i
$677$	−363.885	+	630.267i	−0.537496	+	0.930971i	0.461542	+	0.887119i	$0.347296\pi$
$677$	−363.885	+	630.267i	−0.537496	+	0.930971i	−0.999038	+	0.0438525i	$0.986037\pi$
$678$	148.682	−	56.1585i	0.219294	−	0.0828297i
$679$	333.411	+	577.484i	0.491032	+	0.850492i
$680$	−33.8138	+	509.125i	−0.0497262	+	0.748713i
$681$	−156.046	−	83.1159i	−0.229143	−	0.122050i
$682$	−26.4344	+	132.694i	−0.0387601	+	0.194566i
$683$	−839.650			−1.22936			−0.614678	−	0.788778i	$-0.710714\pi$
$683$	−839.650			−1.22936			−0.614678	+	0.788778i	$0.710714\pi$
$684$	52.1118	−	154.705i	0.0761868	−	0.226177i
$685$		−	882.326i		−	1.28807i
$686$	−137.989	+	692.672i	−0.201151	+	1.00973i
$687$	−276.130	−	442.612i	−0.401936	−	0.644267i
$688$	246.311	+	923.522i	0.358011	+	1.34233i
$689$	−471.687	+	272.329i	−0.684597	+	0.395252i
$690$	100.477	+	82.2630i	0.145619	+	0.119222i
$691$	624.218	+	360.393i	0.903355	+	0.521552i	0.878287	−	0.478133i	$-0.158686\pi$
$691$	624.218	+	360.393i	0.903355	+	0.521552i	0.0250679	+	0.999686i	$0.492020\pi$
$692$	433.755	−	332.433i	0.626813	−	0.480395i
$693$	−358.265	−	532.807i	−0.516976	−	0.768841i
$694$	−422.580	+	143.310i	−0.608905	+	0.206499i
$695$	915.305	+	528.451i	1.31699	+	0.760362i
$696$	−272.045	+	145.618i	−0.390869	+	0.209221i
$697$	−321.418	−	556.712i	−0.461144	−	0.798726i
$698$	64.5870	−	73.6044i	0.0925316	−	0.105450i
$699$	373.738	−	12.7810i	0.534675	−	0.0182848i
$700$	−55.7382	−	425.275i	−0.0796259	−	0.607536i
$701$	−482.229			−0.687916			−0.343958	−	0.938985i	$-0.611768\pi$
$701$	−482.229			−0.687916			−0.343958	+	0.938985i	$0.611768\pi$
$702$	−1098.97	+	503.363i	−1.56548	+	0.717042i
$703$	−104.466			−0.148600
$704$	985.829	+	131.529i	1.40033	+	0.186831i
$705$	−773.265	+	26.4440i	−1.09683	+	0.0375093i
$706$	−50.0059	+	56.9875i	−0.0708299	+	0.0807189i
$707$	−219.362	−	379.945i	−0.310271	−	0.537405i
$708$	491.418	−	81.5781i	0.694093	−	0.115223i
$709$	406.899	+	234.923i	0.573906	+	0.331345i	0.758708	−	0.651431i	$-0.225831\pi$
$709$	406.899	+	234.923i	0.573906	+	0.331345i	−0.184802	+	0.982776i	$0.559164\pi$
$710$	267.178	+	787.829i	0.376307	+	1.10962i
$711$	4.41033	−	9.00948i	0.00620300	−	0.0126716i
$712$	−70.8699	−	47.4428i	−0.0995364	−	0.0666332i
$713$	11.7336	+	6.77440i	0.0164567	+	0.00950127i
$714$	−195.474	−	160.039i	−0.273772	−	0.224144i
$715$	2094.90	−	1209.49i	2.92993	−	1.69160i
$716$	289.796	+	120.234i	0.404743	+	0.167925i
$717$	204.484	+	327.770i	0.285194	+	0.457140i
$718$	1055.71	+	210.312i	1.47035	+	0.292913i
$719$			933.168i			1.29787i	0.760844	+	0.648934i	$0.224785\pi$
$719$			933.168i			1.29787i	−0.760844	+	0.648934i	$0.775215\pi$
$720$	−193.628	+	982.474i	−0.268927	+	1.36455i
$721$	−471.053			−0.653333
$722$	−133.025	+	667.753i	−0.184246	+	0.924866i
$723$	−694.399	−	369.862i	−0.960441	−	0.511565i
$724$	363.480	−	876.083i	0.502044	−	1.21006i
$725$	150.154	+	260.075i	0.207109	+	0.358724i
$726$	−255.455	−	676.326i	−0.351867	−	0.931579i
$727$	−411.433	+	712.622i	−0.565932	+	0.980223i	0.431030	+	0.902337i	$0.358150\pi$
$727$	−411.433	+	712.622i	−0.565932	+	0.980223i	−0.996962	+	0.0778855i	$0.975183\pi$
$728$	−683.140	−	457.318i	−0.938378	−	0.628184i
$729$	−713.720	+	148.477i	−0.979039	+	0.203672i
$730$	−709.771	+	240.706i	−0.972289	+	0.329734i
$731$	273.953	−	474.501i	0.374765	−	0.649112i
$732$	370.599	−	304.690i	0.506283	−	0.416243i
$733$	−747.781	+	431.731i	−1.02016	+	0.588992i	−0.914152	−	0.405372i	$-0.867142\pi$
$733$	−747.781	+	431.731i	−1.02016	+	0.588992i	−0.106013	+	0.994365i	$0.533809\pi$
$734$	175.245	+	153.775i	0.238753	+	0.209503i
$735$	−514.191	−	273.876i	−0.699579	−	0.372621i
$736$	44.1783	−	89.2590i	0.0600249	−	0.121276i
$737$		−	436.797i		−	0.592669i
$738$	−485.850	−	1164.28i	−0.658333	−	1.57761i
$739$		−	377.321i		−	0.510583i	−0.966864	−	0.255292i	$-0.917829\pi$
$739$		−	377.321i		−	0.510583i	0.966864	−	0.255292i	$-0.0821714\pi$
$740$	635.372	−	83.2742i	0.858611	−	0.112533i
$741$	−258.360	+	161.182i	−0.348664	+	0.217519i
$742$	−167.919	−	147.347i	−0.226306	−	0.198581i
$743$	670.266	−	386.978i	0.902108	−	0.520832i	0.0242246	−	0.999707i	$-0.492288\pi$
$743$	670.266	−	386.978i	0.902108	−	0.520832i	0.877884	+	0.478874i	$0.158955\pi$
$744$	−3.35672	+	104.426i	−0.00451172	+	0.140357i
$745$	340.914	−	590.481i	0.457603	−	0.792592i
$746$	−87.0617	−	256.720i	−0.116705	−	0.344128i
$747$	−315.572	+	644.654i	−0.422452	+	0.862991i
$748$	−346.808	−	452.511i	−0.463647	−	0.604961i
$749$	−53.4272	+	92.5386i	−0.0713313	+	0.123549i
$750$	−67.6193	−	11.0827i	−0.0901590	−	0.0147770i
$751$	598.825	+	1037.20i	0.797370	+	1.38109i	0.921323	+	0.388798i	$0.127109\pi$
$751$	598.825	+	1037.20i	0.797370	+	1.38109i	−0.123953	+	0.992288i	$0.539557\pi$
$752$	152.920	+	573.358i	0.203351	+	0.762444i
$753$	−23.2912	−	681.071i	−0.0309312	−	0.904476i
$754$	564.499	+	112.456i	0.748673	+	0.149146i
$755$	−1387.64			−1.83794
$756$	−340.294	−	360.572i	−0.450124	−	0.476947i
$757$			400.054i			0.528473i	0.964458	+	0.264236i	$0.0851199\pi$
$757$			400.054i			0.528473i	−0.964458	+	0.264236i	$0.914880\pi$
$758$	573.767	+	114.302i	0.756948	+	0.150794i
$759$	−145.011	+	4.95908i	−0.191056	+	0.00653371i
$760$	−16.7177	+	251.714i	−0.0219970	+	0.331202i
$761$	539.091	−	311.245i	0.708399	−	0.408994i	−0.102069	−	0.994777i	$-0.532546\pi$
$761$	539.091	−	311.245i	0.708399	−	0.408994i	0.810468	+	0.585783i	$0.199213\pi$
$762$	−63.2439	−	10.3656i	−0.0829972	−	0.0136031i
$763$	332.071	+	191.721i	0.435217	+	0.251273i
$764$	620.157	+	809.174i	0.811724	+	1.05913i
$765$	476.353	−	320.304i	0.622684	−	0.418698i
$766$	170.714	+	503.386i	0.222864	+	0.657162i
$767$	−804.731	−	464.612i	−1.04919	−	0.605752i
$768$	767.610	−	24.4714i	0.999492	−	0.0318637i
$769$	−85.2885	−	147.724i	−0.110908	−	0.192099i	0.805228	−	0.592965i	$-0.202043\pi$
$769$	−85.2885	−	147.724i	−0.110908	−	0.192099i	−0.916137	+	0.400866i	$0.868709\pi$
$770$	745.777	+	654.411i	0.968541	+	0.849884i
$771$	−27.5502	−	44.1605i	−0.0357331	−	0.0572769i
$772$	−153.033	−	1167.62i	−0.198229	−	1.51246i
$773$	26.7288			0.0345780			0.0172890	−	0.999851i	$-0.494496\pi$
$773$	26.7288			0.0345780			0.0172890	+	0.999851i	$0.494496\pi$
$774$	652.344	−	854.796i	0.842821	−	1.10439i
$775$	101.683			0.131204
$776$	513.053	+	1042.65i	0.661150	+	1.34362i
$777$	−149.153	+	280.028i	−0.191960	+	0.360396i
$778$	−212.738	−	186.675i	−0.273442	−	0.239942i
$779$	−158.911	−	275.241i	−0.203993	−	0.353326i
$780$	1442.89	−	1186.28i	1.84986	−	1.52087i
$781$	−804.993	−	464.763i	−1.03072	−	0.595087i
$782$	−54.0666	+	18.3357i	−0.0691389	+	0.0234472i
$783$	316.819	+	141.880i	0.404622	+	0.181200i
$784$	−116.142	+	431.450i	−0.148141	+	0.550319i
$785$	−1347.75	−	778.125i	−1.71688	−	0.991242i
$786$	508.153	+	1345.35i	0.646504	+	1.71164i
$787$	552.776	−	319.145i	0.702384	−	0.405522i	−0.105851	−	0.994382i	$-0.533757\pi$
$787$	552.776	−	319.145i	0.702384	−	0.405522i	0.808235	+	0.588860i	$0.200423\pi$
$788$	−786.415	−	326.277i	−0.997989	−	0.414057i
$789$	66.0208	−	123.951i	0.0836766	−	0.157099i
$790$	−3.02854	+	15.2025i	−0.00383360	+	0.0192437i
$791$		−	121.603i		−	0.153733i
$792$	−561.429	−	967.833i	−0.708875	−	1.22201i
$793$	−894.952			−1.12856
$794$	728.869	+	145.200i	0.917971	+	0.182872i
$795$	430.672	−	268.682i	0.541726	−	0.337964i
$796$	761.567	+	315.968i	0.956742	+	0.396945i
$797$	391.164	+	677.516i	0.490796	+	0.850083i	0.999944	−	0.0105960i	$-0.00337286\pi$
$797$	391.164	+	677.516i	0.490796	+	0.850083i	−0.509148	+	0.860679i	$0.670040\pi$
$798$	−96.6432	−	79.1239i	−0.121107	−	0.0991528i
$799$	170.081	−	294.588i	0.212867	−	0.368696i
$800$	−47.8060	−	745.917i	−0.0597575	−	0.932397i
$801$	6.55454	+	95.7204i	0.00818295	+	0.119501i
$802$	−19.1803	−	56.5570i	−0.0239156	−	0.0705200i
$803$	418.714	−	725.234i	0.521437	−	0.903156i
$804$	−55.2367	−	332.740i	−0.0687024	−	0.413856i
$805$	86.0445	−	49.6778i	0.106888	−	0.0617116i
$806$	128.544	−	146.491i	0.159484	−	0.181751i
$807$	48.6589	+	1422.86i	0.0602961	+	1.76315i
$808$	−337.554	−	685.992i	−0.417764	−	0.849000i
$809$			571.316i			0.706200i	0.935586	+	0.353100i	$0.114873\pi$
$809$			571.316i			0.706200i	−0.935586	+	0.353100i	$0.885127\pi$
$810$	1007.59	−	503.857i	1.24393	−	0.622045i
$811$			554.157i			0.683301i	0.939827	+	0.341651i	$0.110986\pi$
$811$			554.157i			0.683301i	−0.939827	+	0.341651i	$0.889014\pi$
$812$	30.6803	+	234.087i	0.0377836	+	0.288284i
$813$	−1.05599	−	30.8788i	−0.00129888	−	0.0379814i
$814$	−472.251	+	538.185i	−0.580161	+	0.661161i
$815$	866.759	−	500.424i	1.06351	−	0.614017i
$816$	−321.413	−	300.854i	−0.393888	−	0.368693i
$817$	135.444	−	234.596i	0.165782	−	0.287143i
$818$	−684.471	+	232.126i	−0.836762	+	0.283772i
$819$	63.1815	+	922.682i	0.0771446	+	1.12660i
$820$	1185.92	+	1547.37i	1.44624	+	1.88704i
$821$	425.017	−	736.150i	0.517682	−	0.896651i	−0.482108	−	0.876112i	$-0.660129\pi$
$821$	425.017	−	736.150i	0.517682	−	0.896651i	0.999789	−	0.0205386i	$-0.00653811\pi$
$822$	589.046	+	482.265i	0.716601	+	0.586697i
$823$	−299.122	−	518.094i	−0.363453	−	0.629519i	0.625074	−	0.780566i	$-0.285069\pi$
$823$	−299.122	−	518.094i	−0.363453	−	0.629519i	−0.988527	+	0.151047i	$0.951736\pi$
$824$	−819.080	−	54.3996i	−0.994029	−	0.0660190i
$825$	−923.892	+	576.385i	−1.11987	+	0.698648i
$826$	74.4643	−	373.792i	0.0901505	−	0.452533i
$827$	667.626			0.807287			0.403643	−	0.914916i	$-0.367744\pi$
$827$	667.626			0.807287			0.403643	+	0.914916i	$0.367744\pi$
$828$	−109.838	+	22.1156i	−0.132655	+	0.0267097i
$829$		−	1520.09i		−	1.83365i	−0.399291	−	0.916824i	$-0.630744\pi$
$829$		−	1520.09i		−	1.83365i	0.399291	−	0.916824i	$-0.369256\pi$
$830$	216.701	−	1087.78i	0.261085	−	1.31058i
$831$	543.065	−	1019.58i	0.653508	−	1.22693i
$832$	−1135.05	−	874.089i	−1.36424	−	1.05059i
$833$	221.814	−	128.065i	0.266284	−	0.153739i
$834$	−853.088	+	322.220i	−1.02289	+	0.386355i
$835$	−1618.94	−	934.698i	−1.93886	−	1.11940i
$836$	−171.464	−	223.724i	−0.205100	−	0.267612i
$837$	95.2408	−	68.8818i	0.113788	−	0.0822960i
$838$	371.941	−	126.137i	0.443844	−	0.150522i
$839$	−719.550	−	415.432i	−0.857628	−	0.495152i	0.00558927	−	0.999984i	$-0.498221\pi$
$839$	−719.550	−	415.432i	−0.857628	−	0.495152i	−0.863217	+	0.504833i	$0.831554\pi$
$840$	650.868	+	404.202i	0.774843	+	0.481193i
$841$	337.850	+	585.173i	0.401724	+	0.695806i
$842$	125.976	−	143.565i	0.149616	−	0.170504i
$843$	14.9790	−	28.1223i	0.0177686	−	0.0333598i
$844$	−33.4026	+	4.37786i	−0.0395765	+	0.00518704i
$845$	−2309.18			−2.73275
$846$	405.000	−	530.690i	0.478723	−	0.627293i
$847$	−553.149			−0.653069
$848$	−274.965	−	275.603i	−0.324251	−	0.325003i
$849$	599.037	+	960.201i	0.705579	+	1.13098i
$850$	−282.601	+	322.057i	−0.332472	+	0.378891i
$851$	35.8497	+	62.0934i	0.0421265	+	0.0729653i
$852$	−671.995	−	252.245i	−0.788726	−	0.296063i
$853$	1145.57	+	661.395i	1.34299	+	0.775376i	0.987245	−	0.159207i	$-0.0508939\pi$
$853$	1145.57	+	661.395i	1.34299	+	0.775376i	0.355745	+	0.934583i	$0.384227\pi$
$854$	−117.893	−	347.633i	−0.138048	−	0.407064i
$855$	235.511	−	158.360i	0.275452	−	0.185217i
$856$	−103.587	+	154.738i	−0.121013	+	0.180769i
$857$	439.392	+	253.683i	0.512709	+	0.296013i	0.733947	−	0.679207i	$-0.237676\pi$
$857$	439.392	+	253.683i	0.512709	+	0.296013i	−0.221237	+	0.975220i	$0.571010\pi$
$858$	−337.576	+	2059.66i	−0.393445	+	2.40053i
$859$	−169.177	+	97.6744i	−0.196947	+	0.113707i	−0.595230	−	0.803555i	$-0.702939\pi$
$859$	−169.177	+	97.6744i	−0.196947	+	0.113707i	0.398284	+	0.917262i	$0.369606\pi$
$860$	−636.778	+	1534.81i	−0.740440	+	1.78466i
$861$	−964.691	+	32.9904i	−1.12043	+	0.0383164i
$862$	−465.378	−	92.7094i	−0.539881	−	0.107551i
$863$		−	772.315i		−	0.894919i	−0.894304	−	0.447460i	$-0.852329\pi$
$863$		−	772.315i		−	0.894919i	0.894304	−	0.447460i	$-0.147671\pi$
$864$	−550.072	−	666.271i	−0.636657	−	0.771147i
$865$	950.075			1.09835
$866$	70.6026	−	354.407i	0.0815272	−	0.409246i
$867$	−21.0068	−	614.273i	−0.0242293	−	0.708503i
$868$	73.8361	+	30.6340i	0.0850646	+	0.0352926i
$869$	−8.66017	−	14.9999i	−0.00996567	−	0.0172611i
$870$	−529.377	−	86.7643i	−0.608479	−	0.0997290i
$871$	−314.590	+	544.885i	−0.361182	+	0.625586i
$872$	555.272	+	371.719i	0.636780	+	0.426283i
$873$	574.777	−	1174.16i	0.658393	−	1.34497i
$874$	−26.7308	+	9.06526i	−0.0305844	+	0.0103721i
$875$	−26.2134	+	45.4030i	−0.0299582	+	0.0518891i
$876$	227.253	−	605.413i	0.259421	−	0.691111i
$877$	879.427	−	507.737i	1.00277	−	0.578948i	0.0937011	−	0.995600i	$-0.470130\pi$
$877$	879.427	−	507.737i	1.00277	−	0.578948i	0.909066	+	0.416653i	$0.136797\pi$
$878$	279.678	+	245.415i	0.318540	+	0.279516i
$879$	−633.008	+	394.912i	−0.720146	+	0.449274i
$880$	1221.20	+	1224.03i	1.38773	+	1.39095i
$881$			743.678i			0.844130i	0.906566	+	0.422065i	$0.138695\pi$
$881$			743.678i			0.844130i	−0.906566	+	0.422065i	$0.861305\pi$
$882$	463.890	−	193.580i	0.525952	−	0.219479i
$883$			483.566i			0.547640i	0.961781	+	0.273820i	$0.0882872\pi$
$883$			483.566i			0.547640i	−0.961781	+	0.273820i	$0.911713\pi$
$884$	106.721	+	814.265i	0.120725	+	0.921114i
$885$	764.355	+	407.123i	0.863678	+	0.460026i
$886$	423.949	+	372.011i	0.478498	+	0.419877i
$887$	−1096.70	+	633.179i	−1.23641	+	0.713844i	−0.968359	−	0.249560i	$-0.919714\pi$
$887$	−1096.70	+	633.179i	−1.23641	+	0.713844i	−0.268054	+	0.963404i	$0.586381\pi$
$888$	−291.690	+	469.695i	−0.328480	+	0.528935i
$889$	−24.5172	+	42.4651i	−0.0275784	+	0.0477672i
$890$	−47.6178	−	140.411i	−0.0535032	−	0.157765i
$891$	−474.903	+	1165.72i	−0.533000	+	1.30833i
$892$	1378.92	−	1056.81i	1.54587	−	1.18477i
$893$	84.0887	−	145.646i	0.0941643	−	0.163097i
$894$	207.870	+	550.344i	0.232517	+	0.615597i
$895$	272.725	+	472.373i	0.304720	+	0.527791i
$896$	190.007	−	556.040i	0.212062	−	0.620581i
$897$	184.467	+	98.2536i	0.205649	+	0.109536i
$898$	−311.327	−	62.0206i	−0.346690	−	0.0690652i
$899$	−55.9702			−0.0622583
$900$	−630.907	+	555.908i	−0.701007	+	0.617675i
$901$			223.168i			0.247690i
$902$	−2136.36	−	425.592i	−2.36847	−	0.471831i
$903$	−435.468	−	698.015i	−0.482246	−	0.772995i
$904$	14.0433	−	211.446i	0.0155346	−	0.233901i
$905$	1428.03	−	824.474i	1.57794	−	0.911021i
$906$	758.463	−	926.398i	0.837155	−	1.02251i
$907$	−1283.82	−	741.212i	−1.41545	−	0.817213i	−0.419560	−	0.907728i	$-0.637816\pi$
$907$	−1283.82	−	741.212i	−1.41545	−	0.817213i	−0.995895	+	0.0905144i	$0.971149\pi$
$908$	−187.104	+	143.398i	−0.206062	+	0.157928i
$909$	−378.164	+	772.518i	−0.416022	+	0.849855i
$910$	−459.005	−	1353.47i	−0.504401	−	1.48733i
$911$	−982.545	−	567.273i	−1.07853	−	0.622692i	−0.148034	−	0.988982i	$-0.547294\pi$
$911$	−982.545	−	567.273i	−1.07853	−	0.622692i	−0.930501	+	0.366290i	$0.880628\pi$
$912$	−158.908	−	148.744i	−0.174241	−	0.163096i
$913$	619.660	+	1073.28i	0.678708	+	1.17556i
$914$	−640.947	−	562.423i	−0.701255	−	0.615343i
$915$	833.591	−	28.5071i	0.911028	−	0.0311553i
$916$	−689.679	+	90.3918i	−0.752925	+	0.0986810i
$917$	1100.33			1.19992
$918$	−46.5298	+	493.089i	−0.0506860	+	0.537134i
$919$	−51.6557			−0.0562086			−0.0281043	−	0.999605i	$-0.508947\pi$
$919$	−51.6557			−0.0562086			−0.0281043	+	0.999605i	$0.508947\pi$
$920$	155.354	−	76.4442i	0.168863	−	0.0830916i
$921$	−1671.97	+	57.1778i	−1.81538	+	0.0620823i
$922$	−610.423	−	535.639i	−0.662064	−	0.580953i
$923$	669.462	+	1159.54i	0.725311	+	1.25628i
$924$	−844.518	+	140.195i	−0.913981	+	0.151726i
$925$	466.010	+	269.051i	0.503794	+	0.290866i
$926$	1354.77	−	459.446i	1.46304	−	0.496162i
$927$	515.306	+	766.357i	0.555885	+	0.826706i
$928$	26.3141	+	410.579i	0.0283557	+	0.442435i
$929$	−781.777	−	451.359i	−0.841525	−	0.485855i	0.0162571	−	0.999868i	$-0.494825\pi$
$929$	−781.777	−	451.359i	−0.841525	−	0.485855i	−0.857782	+	0.514013i	$0.828158\pi$
$930$	−115.065	+	140.542i	−0.123726	+	0.151120i
$931$	109.666	−	63.3158i	0.117794	−	0.0680084i
$932$	191.076	−	460.543i	0.205017	−	0.494145i
$933$	228.138	+	365.684i	0.244521	+	0.391944i
$934$	−163.731	+	821.887i	−0.175301	+	0.879965i
$935$		−	991.158i		−	1.06006i
$936$	3.30560	+	1611.68i	0.00353163	+	1.72188i
$937$	1400.55			1.49471			0.747356	−	0.664424i	$-0.231323\pi$
$937$	1400.55			1.49471			0.747356	+	0.664424i	$0.231323\pi$
$938$	−253.095	−	50.4199i	−0.269824	−	0.0537526i
$939$	717.321	+	382.071i	0.763920	+	0.406891i
$940$	−395.336	+	952.866i	−0.420571	+	1.01369i
$941$	−607.305	−	1051.88i	−0.645383	−	1.11784i	−0.984213	−	0.176989i	$-0.943364\pi$
$941$	−607.305	−	1051.88i	−0.645383	−	1.11784i	0.338830	−	0.940848i	$-0.389969\pi$
$942$	1256.14	−	474.457i	1.33348	−	0.503669i
$943$	−109.067	+	188.910i	−0.115660	+	0.200329i
$944$	172.648	−	641.360i	0.182890	−	0.679407i
$945$	−88.2398	−	857.407i	−0.0933755	−	0.907309i
$946$	−596.295	−	1758.30i	−0.630333	−	1.85867i
$947$	−9.83190	+	17.0293i	−0.0103821	+	0.0179824i	−0.871170	−	0.490982i	$-0.836638\pi$
$947$	−9.83190	+	17.0293i	−0.0103821	+	0.0179824i	0.860788	+	0.508964i	$0.169971\pi$
$948$	−8.49394	−	10.3313i	−0.00895985	−	0.0108980i
$949$	−1044.65	+	603.132i	−1.10079	+	0.635544i
$950$	−139.720	+	159.227i	−0.147073	+	0.167607i
$951$	808.643	+	430.713i	0.850308	+	0.452905i
$952$	−302.233	+	148.719i	−0.317471	+	0.156217i
$953$			1678.28i			1.76105i	0.473997	+	0.880526i	$0.342811\pi$
$953$			1678.28i			1.76105i	−0.473997	+	0.880526i	$0.657189\pi$
$954$	−56.0249	+	434.376i	−0.0587264	+	0.455321i
$955$			1772.38i			1.85589i
$956$	510.732	−	66.9384i	0.534238	−	0.0700192i
$957$	508.543	−	317.263i	0.531393	−	0.331518i
$958$	41.3519	−	47.1253i	0.0431648	−	0.0491913i
$959$	504.434	−	291.235i	0.526000	−	0.303686i
$960$	1085.07	+	778.003i	1.13028	+	0.810420i
$961$	471.024	−	815.838i	0.490140	−	0.848947i
$962$	976.723	−	331.238i	1.01530	−	0.344322i
$963$	208.997	−	14.3113i	0.217027	−	0.0148611i
$964$	−832.605	+	638.115i	−0.863698	+	0.661945i
$965$	1023.63	−	1772.98i	1.06076	−	1.83729i
$966$	−13.8653	+	84.5969i	−0.0143533	+	0.0875744i
$967$	122.729	+	212.572i	0.126917	+	0.219827i	0.922481	−	0.386043i	$-0.126158\pi$
$967$	122.729	+	212.572i	0.126917	+	0.219827i	−0.795564	+	0.605870i	$0.792825\pi$
$968$	−961.831	−	63.8805i	−0.993627	−	0.0659923i
$969$	4.26446	+	124.699i	0.00440088	+	0.128689i
$970$	−394.695	+	1981.27i	−0.406902	+	2.04255i
$971$	−91.7515			−0.0944918			−0.0472459	−	0.998883i	$-0.515044\pi$
$971$	−91.7515			−0.0944918			−0.0472459	+	0.998883i	$0.515044\pi$
$972$	−214.353	+	948.070i	−0.220527	+	0.975381i
$973$			697.718i			0.717079i
$974$	−61.3370	+	307.896i	−0.0629743	+	0.316115i
$975$	1567.64	−	53.6099i	1.60783	−	0.0549845i
$976$	−164.850	−	618.088i	−0.168903	−	0.633287i
$977$	−1148.46	+	663.066i	−1.17550	+	0.678675i	−0.954969	−	0.296705i	$-0.904112\pi$
$977$	−1148.46	+	663.066i	−1.17550	+	0.678675i	−0.220531	+	0.975380i	$0.570779\pi$
$978$	−139.671	+	852.177i	−0.142813	+	0.871347i
$979$	143.470	+	82.8325i	0.146548	+	0.0846093i
$980$	−616.530	+	472.514i	−0.629113	+	0.482157i
$981$	−51.3554	−	749.978i	−0.0523501	−	0.764504i
$982$	57.3271	−	19.4414i	0.0583779	−	0.0197978i
$983$	1197.01	+	691.093i	1.21771	+	0.703045i	0.964427	−	0.264348i	$-0.0851567\pi$
$983$	1197.01	+	691.093i	1.21771	+	0.703045i	0.253282	+	0.967393i	$0.418490\pi$
$984$	−1681.24	−	54.0429i	−1.70858	−	0.0549216i
$985$	−740.089	−	1281.87i	−0.751359	−	1.30139i
$986$	155.554	−	177.272i	0.157762	−	0.179789i
$987$	−270.355	−	433.354i	−0.273916	−	0.439062i
$988$	52.7632	+	402.577i	0.0534040	+	0.407466i
$989$	−185.922			−0.187990
$990$	248.823	−	1929.19i	0.251337	−	1.94868i
$991$	−1113.50			−1.12362			−0.561808	−	0.827267i	$-0.689894\pi$
$991$	−1113.50			−1.12362			−0.561808	+	0.827267i	$0.689894\pi$
$992$	124.850	+	61.7942i	0.125857	+	0.0622925i
$993$	605.345	−	1136.51i	0.609612	−	1.14452i
$994$	−362.220	+	412.792i	−0.364407	+	0.415284i
$995$	716.704	+	1241.37i	0.720306	+	1.24761i
$996$	607.766	+	739.236i	0.610206	+	0.742205i
$997$	603.984	+	348.711i	0.605802	+	0.349760i	0.771321	−	0.636447i	$-0.219597\pi$
$997$	603.984	+	348.711i	0.605802	+	0.349760i	−0.165519	+	0.986207i	$0.552930\pi$
$998$	−68.3524	−	201.551i	−0.0684894	−	0.201955i
$999$	618.742	−	63.6777i	0.619361	−	0.0637414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.12	yes	44
3.2	odd	2		216.3.j.a.197.11		44
4.3	odd	2		288.3.n.a.209.12		44
8.3	odd	2		288.3.n.a.209.11		44
8.5	even	2	inner	72.3.j.a.29.18	yes	44
9.2	odd	6		648.3.h.a.485.6		44
9.4	even	3		216.3.j.a.125.5		44
9.5	odd	6	inner	72.3.j.a.5.18	yes	44
9.7	even	3		648.3.h.a.485.39		44
12.11	even	2		864.3.n.a.305.19		44
24.5	odd	2		216.3.j.a.197.5		44
24.11	even	2		864.3.n.a.305.4		44
36.7	odd	6		2592.3.h.a.1457.38		44
36.11	even	6		2592.3.h.a.1457.7		44
36.23	even	6		288.3.n.a.113.11		44
36.31	odd	6		864.3.n.a.17.4		44
72.5	odd	6	inner	72.3.j.a.5.12	✓	44
72.11	even	6		2592.3.h.a.1457.37		44
72.13	even	6		216.3.j.a.125.11		44
72.29	odd	6		648.3.h.a.485.40		44
72.43	odd	6		2592.3.h.a.1457.8		44
72.59	even	6		288.3.n.a.113.12		44
72.61	even	6		648.3.h.a.485.5		44
72.67	odd	6		864.3.n.a.17.19		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.12	✓	44	72.5	odd	6	inner
72.3.j.a.5.18	yes	44	9.5	odd	6	inner
72.3.j.a.29.12	yes	44	1.1	even	1	trivial
72.3.j.a.29.18	yes	44	8.5	even	2	inner
216.3.j.a.125.5		44	9.4	even	3
216.3.j.a.125.11		44	72.13	even	6
216.3.j.a.197.5		44	24.5	odd	2
216.3.j.a.197.11		44	3.2	odd	2
288.3.n.a.113.11		44	36.23	even	6
288.3.n.a.113.12		44	72.59	even	6
288.3.n.a.209.11		44	8.3	odd	2
288.3.n.a.209.12		44	4.3	odd	2
648.3.h.a.485.5		44	72.61	even	6
648.3.h.a.485.6		44	9.2	odd	6
648.3.h.a.485.39		44	9.7	even	3
648.3.h.a.485.40		44	72.29	odd	6
864.3.n.a.17.4		44	36.31	odd	6
864.3.n.a.17.19		44	72.67	odd	6
864.3.n.a.305.4		44	24.11	even	2
864.3.n.a.305.19		44	12.11	even	2
2592.3.h.a.1457.7		44	36.11	even	6
2592.3.h.a.1457.8		44	72.43	odd	6
2592.3.h.a.1457.37		44	72.11	even	6
2592.3.h.a.1457.38		44	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.390748 + 1.96146i) q^{2} +(-0.102534 - 2.99825i) q^{3} +(-3.69463 - 1.53287i) q^{4} +(-3.47699 - 6.02232i) q^{5} +(5.92100 + 0.970445i) q^{6} +(2.29534 - 3.97565i) q^{7} +(4.45034 - 6.64790i) q^{8} +(-8.97897 + 0.614843i) q^{9} +O(q^{10})\)	\(q+(-0.390748 + 1.96146i) q^{2} +(-0.102534 - 2.99825i) q^{3} +(-3.69463 - 1.53287i) q^{4} +(-3.47699 - 6.02232i) q^{5} +(5.92100 + 0.970445i) q^{6} +(2.29534 - 3.97565i) q^{7} +(4.45034 - 6.64790i) q^{8} +(-8.97897 + 0.614843i) q^{9} +(13.1711 - 4.46675i) q^{10} +(-7.77003 + 13.4581i) q^{11} +(-4.21711 + 11.2346i) q^{12} +(19.3855 - 11.1922i) q^{13} +(6.90117 + 6.05570i) q^{14} +(-17.6999 + 11.0424i) q^{15} +(11.3006 + 11.3268i) q^{16} -9.17185i q^{17} +(2.30253 - 17.8521i) q^{18} -4.53461i q^{19} +(3.61474 + 27.5800i) q^{20} +(-12.1553 - 6.47437i) q^{21} +(-23.3614 - 20.4993i) q^{22} +(-2.69533 + 1.55615i) q^{23} +(-20.3883 - 12.6616i) q^{24} +(-11.6789 + 20.2284i) q^{25} +(14.3782 + 42.3973i) q^{26} +(2.76410 + 26.8581i) q^{27} +(-14.5746 + 11.1701i) q^{28} +(6.42846 - 11.1344i) q^{29} +(-14.7429 - 39.0324i) q^{30} +(-2.17666 - 3.77008i) q^{31} +(-26.6327 + 17.7397i) q^{32} +(41.1474 + 21.9166i) q^{33} +(17.9902 + 3.58388i) q^{34} -31.9235 q^{35} +(34.1165 + 11.4920i) q^{36} -23.0374i q^{37} +(8.89444 + 1.77189i) q^{38} +(-35.5448 - 56.9751i) q^{39} +(-55.5095 - 3.68669i) q^{40} +(60.6979 - 35.0439i) q^{41} +(17.4489 - 21.3123i) q^{42} +(51.7345 + 29.8689i) q^{43} +(49.3370 - 37.8122i) q^{44} +(34.9226 + 51.9364i) q^{45} +(-1.99913 - 5.89484i) q^{46} +(32.1187 + 18.5438i) q^{47} +(32.8019 - 35.0434i) q^{48} +(13.9628 + 24.1843i) q^{49} +(-35.1136 - 30.8118i) q^{50} +(-27.4995 + 0.940424i) q^{51} +(-88.7787 + 11.6357i) q^{52} -24.3319 q^{53} +(-53.7612 - 5.07311i) q^{54} +108.065 q^{55} +(-16.2147 - 32.9522i) q^{56} +(-13.5959 + 0.464951i) q^{57} +(19.3278 + 16.9599i) q^{58} +(-20.7560 - 35.9504i) q^{59} +(82.3211 - 13.6658i) q^{60} +(-34.6245 - 19.9904i) q^{61} +(8.24537 - 2.79626i) q^{62} +(-18.1654 + 37.1086i) q^{63} +(-24.3890 - 59.1707i) q^{64} +(-134.807 - 77.8306i) q^{65} +(-59.0667 + 72.1450i) q^{66} +(-24.3421 + 14.0539i) q^{67} +(-14.0593 + 33.8866i) q^{68} +(4.94209 + 7.92171i) q^{69} +(12.4741 - 62.6167i) q^{70} +59.8148i q^{71} +(-35.8720 + 62.4275i) q^{72} -53.8883 q^{73} +(45.1869 + 9.00183i) q^{74} +(61.8472 + 32.9420i) q^{75} +(-6.95098 + 16.7537i) q^{76} +(35.6698 + 61.7819i) q^{77} +(125.643 - 47.4567i) q^{78} +(-0.557280 + 0.965237i) q^{79} +(28.9215 - 107.439i) q^{80} +(80.2439 - 11.0413i) q^{81} +(45.0196 + 132.750i) q^{82} +(39.8750 - 69.0655i) q^{83} +(34.9851 + 42.5530i) q^{84} +(-55.2358 + 31.8904i) q^{85} +(-78.8017 + 89.8037i) q^{86} +(-34.0429 - 18.1325i) q^{87} +(54.8887 + 111.547i) q^{88} -10.6605i q^{89} +(-115.517 + 48.2050i) q^{90} -102.760i q^{91} +(12.3436 - 1.61780i) q^{92} +(-11.0804 + 6.91271i) q^{93} +(-48.9231 + 55.7536i) q^{94} +(-27.3089 + 15.7668i) q^{95} +(55.9188 + 78.0326i) q^{96} +(-72.6276 + 125.795i) q^{97} +(-52.8923 + 17.9375i) q^{98} +(61.4923 - 125.617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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